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3.8 million more workers filed for unemployment benefits last week. That’s probably an undercount.

The figures announced Thursday by the Labor Department bring the number of workers joining the official jobless ranks in the last six weeks to more than 30 million, and underscore just how dire economic conditions remain.

Many state agencies still find themselves overwhelmed by the flood of claims, leaving perhaps millions with dwindling resources to pay the rent or put food on the table.

If anything, the job losses may be far worse than government figures indicate, according to many economists. A study by the Economic Policy Institute found that roughly 50 percent more people than counted as filing claims in a recent four-week period may have qualified for benefits but were stymied in applying or didn’t even try because they found the process too formidable.

“The problem is even bigger than the data suggest,” said Elise Gould, a senior economist with the institute, a left-leaning research group. “We’re undercounting the economic pain.”

As Emily Badger and Alicia Parlapiano reported, systems that were devised to treat each unemployment case as potentially fraudulent are now rushing to deal with millions of newly unemployed people.

The state unemployment systems that were supposed to help millions of jobless workers were full of boxes to check and mandates to meet that couldn’t possibly apply in a pandemic.

States required workers to document their job searches, weekly; to register with employment services, in person; to take a wait period before their first check, up to 10 days.

Such requirements increased in the years following the Great Recession, as many states moved to tighten access to or reduce unemployment benefits. With them, most states cut the share of jobless workers they helped.

Now these requirements have been getting in the way. Effectively, many states have been trying to scale up aid with systems built to keep claims low.

Stocks dip as jobless claims rack up.

U.S. stocks followed European markets on Thursday, dipping as investors considered data revealing a sharp contraction in the eurozone economy and another surge of jobless claims in the United States.

The S&P 500 was down more than 1 percent on Thursday afternoon. European markets fell about 2 percent after a rally in Asia.

Adding to the bleak economic news, the Commerce Department reported on Thursday that consumer spending in March fell by 7.5 percent from February’s level, a stunning decline that helps explain why the overall economy is so weak. Consumer activity is responsible for two-thirds of the country’s economic performance.

The data came a day after the government said U.S. gross domestic product, the broadest measure of goods and services produced in the economy, fell at a 4.8 percent annual rate in the first quarter of the year, the Commerce Department said Wednesday. That is the first decline since 2014, and the worst quarterly contraction since the country was in a deep recession more than a decade ago.

On Wednesday, the S&P 500 had gained nearly 3 percent, lifted by news that the drugmaker Gilead Science had seen early results that its experimental drug remdesivir could speed recovery in patients infected with the coronavirus. A steady climb has lifted the S&P 500 by more than 31 percent since its March 23 low.

Millions more Americans will soon be able to sit down to eat at restaurants, browse in person at retail stores or make appointments to get their hair cut, as a number of states move toward reopening on Thursday, despite warnings from public health experts.

Governors in several states — including Alabama, Maine, Tennessee and Texas — plan to allow stay-at-home orders to expire on Thursday, paving the way for certain businesses to reopen and marking the end of an unparalleled month in which an astonishing nine in 10 residents in the United States were told to stay at home to help stop the spread of the virus.

Federal guidelines encouraging people to curtail nearly all public activities are also poised to expire Thursday after President Trump indicated he did not intend to extend them.

“They’ll be fading out, because now the governors are doing it,” Mr. Trump told reporters on Wednesday, referring to the restrictions.

More restrictions will be lifted on Friday as additional states, including Iowa, North Dakota and Wyoming, ease their rules.

The latest reopenings represent a pivotal moment in America’s response to the virus, even as the number of deaths from the virus in the United States has surged past 60,000. As of Friday, more than a dozen states will have begun to partially reopen their economies and restart public life, raising concerns among health experts about another spike in cases that may not be detected in official numbers for two weeks.

Dr. Anthony S. Fauci, the director of the National Institute of Allergy and Infectious Diseases, has warned that premature action by states could lead to “a rebound to get us right back in the same boat that we were in a few weeks ago.”

Texas is expected to take one of the most expansive actions on Friday, allowing retail stores, restaurants, movie theaters and malls to reopen and operate at 25 percent capacity. Gov. Greg Abbott, a Republican, lifted his stay at home order after less than a month, citing the state’s expanded testing, stock of protective equipment and a high number of coronavirus recoveries.

The pace of reopening has created a divided America, along both political and geographical lines. Many states in the South with Republican governors were among the first to partially reopen, including Georgia, Oklahoma and South Carolina, which paved the way last week. Also beginning to reopen are less dense states, including Alaska and Montana. Several of the nation’s most populous states, including California, Michigan, New York and Illinois, remain on extended lockdown.

Dr. Anthony S. Fauci, the director of the National Institute of Allergy and Infectious Diseases, said Thursday that he is optimistic a vaccine could be available in large quantities as early as January.

He said a new research program, known as Warp Speed, will accelerate development of a vaccine. In the next phase, he said Thursday on NBC’s Today, “We’re going to safely and carefully — but as quickly as we possibly can — try and get an answer as to whether it works and is safe.”

If that is the case, he said, in cooperation with the companies involved, the production would start to ramp up, but doing so would be a risk.

“In other words, you don’t wait until you get an answer before you start manufacturing. You, at risk, proactively start making it assuming it’s going to work. And if it does, then you can scale up and hopefully get to that timeline,” he said. “I think that is doable if things fall in the right place.”

The January target, Dr. Fauci said, is consistent with what he was saying in January and February — that a vaccine is 12-18 months away.

Dr. Fauci also repeated his optimism about the potential benefit of the drug remdesivir to help some patients recover faster from the virus. The Federal Drug Administration is expected to approve its use on an emergency basis after promising results from trials.

“This is not the total answer by any means,” Dr. Fauci said. “But it’s a very important first step.”

After pictures of packed California beaches led to an outcry that social distancing guidelines were being flagrantly flouted, California officials are weighing a plan to order all beaches in the state closed beginning on Friday, according to a memo from a police association.

The discussions follow pleas by Gov. Gavin Newsom for Californians to slow the spread of the virus by staying home, despite the temptations of seawater and sunny weather. Photographs of umbrellas and surfers dotting the shoreline of some beaches showed that many residents had not heeded his requests. Mr. Newsom’s office had no comment in advance of a news conference scheduled for Thursday afternoon.

Beaches in warmer parts of the nation have emerged as flash points for weeks, as photos showing social distancing guidelines being recklessly flouted. Photos of crowded beaches in Florida during spring break prompted national outrage.

Now, as spring brings warmer weather all over, beaches are posing a challenge to more coastal states. Many are struggling to find a balance that will allow them to provide safe outdoor spaces to a frustrated, pent-up public, while preventing the kind of large, packed gatherings that can help spread the virus — but which are commonly found on big public beaches.

Even as California weighs closing its beaches, beaches in Galveston, Texas will reopen on Friday — following Gov. Greg Abbott’s phased reopening order, which permits outdoor activities as long as people tale precautions to “minimize in-person contact with people who are not in the same household.”

Mr. Newsom’s office and the state’s Office of Emergency Services had no comment in advance of a midday news conference. However, municipal authorities in Orange County, where the beach issue has been most contentious, said they had seen a notification from the California Police Chiefs Association, which said it was offering “a heads up” to local law enforcement, “to provide time for you to plan for any situations you might expect as a result, knowing each community has its own dynamics.”

Even before the state began considering closing beaches, the flurry of beachgoers last weekend prompted some local governments to take action.

In Northern California, Santa Cruz County on Wednesday said it was closing beaches entirely between the hours of 11 a.m. and 5 p.m., beginning this weekend, and that they would only be open for “recreational activities to promote physical and mental health” outside of that window. Officials there said the order was a direct result of the “overwhelming weekend beach crowds.”

“Despite warnings against traveling to Santa Cruz County for beach access and against congregating on beaches, local law enforcement spent the weekend responding to numerous issues all along our coastline,” Sheriff Jim Hart of Santa Cruz County said in a statement. “Unfortunately, these actions are necessary to protect the health and welfare of our most vulnerable residents.”

Senior Trump administration officials have pushed American spy agencies to hunt for evidence to support an unsubstantiated theory that a government laboratory in Wuhan, China, was the origin of the outbreak, according to current and former American officials. The effort comes as Mr. Trump escalates a public campaign to blame China for the pandemic.

Most intelligence agencies remain skeptical that conclusive evidence of a link to a lab can be found, and scientists who have studied the genetics of the coronavirus say that the overwhelming probability is that it leapt from animal to human in a nonlaboratory setting, as was the case with H.I.V., Ebola and SARS.

Reporting for The New York Times, Mark Mazzetti, Julian E. Barnes, Edward Wong and Adam Goldman investigate how scientists, spies and government officials have wrestled for months with varying theories about how the outbreak began. Many agree on the importance of determining the genesis of the pandemic. In government and academia, however, experts have ruled out the notion that it was concocted as a bioweapon. And they agree that the new pathogen began as a bat virus that evolved naturally, probably in another mammal, to become adept at infecting and killing humans.

A few veteran national security experts have pointed to a history of lab accidents infecting researchers to suggest it might have happened in this case, but many scientists have dismissed such theories.

N.Y.C. subway service will halt between 1 and 5 a.m. so trains can be disinfected.

Gov. Andrew M. Cuomo of New York said Thursday that the New York City subway would halt service from 1 a.m. to 5 a.m. each night so trains could be disinfected.

The policy will go into effect next Wednesday, May 6, the governor said. Public transit in New York City is the only system in the United States, and among the relatively few in the world, that runs 24 hours a day. The system has only shut down twice in the past decade, both times as a result of hurricanes, including Sandy in 2012.

“This is as ambitious as anything we’ve ever undertaken,” the governor said.

He said that shuttle buses, dollar vans and even for-hire vehicles would provide what he called an “essential connector” during those hours to transport essential workers who needed to get to their jobs.

The announcement comes after days of building tension over homeless people using subway trains as an alternative form of shelter and creating what many felt were unsanitary conditions on trains. On Tuesday, Mr. Cuomo, who effectively controls the Metropolitan Transportation Authority, the state agency that runs the transit system, had declared the situation “disgusting.”

The governor said Thursday that Mayor Bill de Blasio would help lead the effort to coordinate transportation during the nightly halt and praised the mayor for his cooperation.

“It’s a heck of an undertaking by the mayor and I applaud him for his ambition here in stepping up and taking this on,” Mr. Cuomo said.

Mr. de Blasio, appearing at the briefing, said that the effort would be a way to help homeless people, whose life on the subways he called “an unacceptable reality.”

The M.T.A. had rolled out new measures to address the use of the subway by the homeless on Wednesday.

Here are some other highlights from the governor’s morning briefing:

  • 306 more people died of the virus in the state, down from 330 reported on Wednesday and the lowest number since March 30.

  • The number of new hospital admissions for virus patients declined, after it ticked up slightly on Wednesday.

  • The number of virus patients in hospitals dropped for the 17th day in a row and is now below 12,000 — down nearly 40 percent from mid-April, when there were nearly 19,000 hospitalized patients.

Mr. Cuomo also gave more details on the state’s planned effort to test and trace the virus, saying that the “massive” effort would require hiring between 6,400 and 17,000 contact tracers, depending on the virus’s spread.

“When social distancing is relaxed, contract tracing is our best hope for isolating the virus when it appears and keeping it isolated,” said Michael R. Bloomberg, the former mayor of New York City, who appeared by video at the governor’s Thursday briefing and who has volunteered to lead the effort.

As more doctors are seeing patients arriving at the hospital with an insidious form of pneumonia, tracking symptoms and paying special attention as the illness nears its second week has taken on new urgency.

Tara Parker-Pope, the founding editor of Well, writes:

Marking your calendar at the first sign of illness, and tracking your fever and oxygen levels, are important steps in monitoring a coronavirus infection. Covid-19, the disease caused by the coronavirus, has been unpredictable in the range of symptoms it can cause. But when it turns serious, it often follows a consistent pattern.

While most patients recover in about a week, a significant minority of patients enter “a very nasty second wave” of illness, said Dr. Ilan Schwartz, assistant professor of infectious disease at the University of Alberta. “After the initial symptoms, things plateau and maybe even improve a little bit, and then there is a secondary worsening.”

While every patient is different, doctors say that days five through 10 of the illness are often the most worrisome time for respiratory complications of Covid-19, particularly for older patients and those with underlying conditions like high blood pressure, obesity or diabetes. Younger patients who develop complications may begin struggling a little later, as late as days 10 to 12. Most people who reach day 14 without any worrying symptoms (other than feeling miserable and fatigued) are likely to be on the road to recovery.

The best way to monitor your health during this time is to use a pulse oximeter, a small device that clips on your finger and measures your blood oxygen levels. (There are phone-based apps meant to do this, but they have tested poorly) The normal oxygen saturation range is about 96 to 99 percent. If your blood oxygen reading drops to 92 percent, it’s time to call a doctor.

As Georgia reopens many businesses over objections from Mr. Trump and others, a new study illustrates the high rates of virus infection among black people in the state.

The report by the Centers for Disease Control and Prevention said that more than four-fifths of the state’s hospitalized virus patients were black, though they were not more likely than other groups to die from the disease or to require a ventilator.

“That is a very high rate of infections,” said Dr. Wayne A.I. Frederick, a cancer surgeon and the president of Howard University, who was not involved in the C.D.C. report. He said the high percentage of black people in the study likely reflects the patients’ occupations.

The sample of patients in the C.D.C. study was taken from eight hospitals in Georgia, including seven in metropolitan Atlanta and one in southern Georgia. Slightly more than half of Atlanta residents are African-American, according to the United States Census Bureau.

The study appeared against the backdrop of a debate over whether Georgia has been premature to ease restrictions on businesses. On Friday, Gov. Brian Kemp allowed hair and nail salons, bowling alleys and tattoo parlors to open again. On Monday, restaurants were permitted to resume dine-in service. Georgia’s stay-at-home order is scheduled to end on Thursday.

A network of conservative leaders, donors and organizations has launched a legal onslaught against state and local restrictions intended to slow the spread of the virus, pushing to allow churches to hold services, businesses to reopen and people to be able to visit with family and friends.

They have been emboldened in recent days by increasing signs of support from a powerful ally: the Justice Department.

Attorney General William P. Barr issued a memorandum this week directing two of his department’s top lawyers to lead an effort with other federal agencies to monitor state and local policies “and, if necessary, take action to correct” those that “could be violating the constitutional rights and civil liberties of individual citizens.”

Though the Justice Department has so far weighed in formally on only one case — a lawsuit by a Baptist church in Greenville, Miss. — the new directive reinforced the message that court challenges to state and local restrictions by Mr. Trump’s allies could get a favorable viewing, and potential support, from the administration.

The guidance raises the prospect that the Trump administration could side with supportive groups in legal challenges against elected state and local leaders who enacted policies that were intended to stave off the spread of the virus. Public health officials fear the virus’s spread could be accelerated by premature lifting of restrictions.

Mayor Eric M. Garcetti of Los Angeles said on Wednesday evening that any city and county resident who wanted a virus test can get one, whether or not they were showing symptoms, making Los Angeles the “first major city in America” to offer free coronavirus testing to all residents.

Priority will still be given to health care employees, other workers who interact with the public and people with symptoms, but asymptomatic residents will also be able to get tests.

“So, if you think you might have Covid-19, want the reassurance that you don’t or you’ve been around people that you have seen with symptoms, get a test,” the mayor said. “We can do it.”

Gov. Gavin Newsom of California had outlined this week how the state might gradually reopen, and Mr. Garcetti said the availability of testing was a “really important step to prepare for other steps forward.”

It is unclear how many people will sign up to be tested or how long they will have to wait. Just over six million people have been tested in the United States, including about 603,000 in California, according to Johns Hopkins University data. More than 10 million people live in Los Angeles County, according to the Census Bureau.

In response to a reporter’s question about how the city would manage to test so many people, Mr. Garcetti said the city had tests left over each day and was confident in its ability to test any resident who wanted it, including those who want to get tested multiple times over the course of several weeks or months.

Mr. Garcetti said the testing would be carried out at 34 sites in the city that have the capacity to test at least 18,000 people each day. At least 140,000 people have been tested at those sites in the past month, he said.

School districts across the country have adapted in myriad ways as the very model of teaching and learning has been transformed. Now another fundamental part of American education is being transformed: the report card.

In many cities and towns, new grading systems for this semester have been created, driven by concern for students who face hardship from the virus and its economic fallout. Some districts have dropped letter grades altogether, while others are guaranteeing A’s in most cases, or ensuring that students’ performance during the pandemic will not count against them.

But there are places where administrators have encountered stiff resistance to the idea of dropping grades, even temporarily. Some parents and students are concerned about the ability of high achievers to compete in selective college admissions, while others worry that eschewing grades means students will have less incentive to participate in remote learning.

The debate been more particularly passionate in the San Mateo Union High School District, south of San Francisco. It is a place that epitomizes the socioeconomic divides that have always characterized American education, with the children of tech executives attending class alongside the children of undocumented gardeners and office cleaners.

An April 16 school board meeting to address grading drew more than 500 people. In public comments delivered via Zoom, many parents and students argued that grades were crucial during the college admissions process. One student said grades provide “compensation and incentive for people to work hard.”

Without letter grades, asked another student, “What motivation do we have to continue working for the end of the school year?”

The pandemic has hit small and independent restaurants hard, forcing owners to shutter dining rooms and lay off employees. But the shutdowns have done more than imperil the restaurants’ financial health — they have made the buildings themselves tempting targets for burglars emboldened by the quiet streets and deserted spaces.

Across the country, closed restaurants have been invaded by thieves who seem especially drawn to well-stocked liquor cabinets, and iPads and other equipment.

“It’s the perfect storm,” said Kam Razavi, an owner of a California restaurant who watched from his phone as security cameras recorded a burglar helping himself to the best bottles in the bar. “They know everybody is probably at home with a loaded gun. They’re not going to go rob homes. They’re going to go to closed businesses.”

When his restaurant was broken into in early April, Mr. Razavi had already laid off most of his 75 or so employees, and was uncertain whether he would ever reopen. Now, he is out $5,000 from stolen alcohol, a broken door and cleanup costs.

Most restaurant owners who have had burglaries expect their insurance companies to cover at least a portion of the damage, though the pandemic has created backlogs for claims, delaying payments in some cases.

Some burglars haven’t gotten far. Shortly after the lockdown in New York, a would-be thief broke into Dinosaur Bar-B-Que, in Harlem, and put a few half-empty bottles of alcohol into a bag. When he came upstairs from the basement, police officers were waiting for him.

Need help figuring out the balance between your screens and your life?

Phones and computers are keeping us tethered to the outside world during the pandemic. But being thoughtful about your use of screens can help you emerge from this crisis empowered and in control, and with more self-awareness.

Follow updates on the pandemic from our team of international correspondents.

South Korea on Thursday reported that for the first time since the virus’s Feb. 29 peak, it had no new domestic cases and just four cases among people who came in from outside the country.

That progress has been mirrored in Hong Kong, which on Thursday reported that there had been no new cases in the semiautonomous Chinese territory for five straight days.

Reporting was contributed by Alan Blinder, Eileen Sullivan, Michael Cooper, Sarah Mervosh, Lisa Lerer, Kenneth P. Vogel, Karen Barrow, Dana Goldstein, Tariro Mzezewa, Jonah Engel Bromwich, Matt Phillips, Brad Plumer, David Waldstein, Alan Feuer, Ashley Southall, Amelia Nierenberg, David Yaffe-Bellany, Michael Gold, Marc Santora, Emily Badger, Alicia Parlapiano and Nicholas Bogel-Burroughs.