Boris Johnson has insisted he “deplores any threats to anybody, particularly female MPs”, after he described one MP’s safety concerns as “humbug”.
The PM also said that “tempers need to come down” in Parliament.
It follows a stormy debate, after MPs returned to Parliament following a Supreme Court decision that the suspension of Parliament was unlawful.
Mr Johnson defended his description of a law seeking to block a no-deal Brexit as “the surrender bill”.
The law, known as the Benn bill, forces the government to ask for an extension to the Brexit deadline.
During a number of interviews with BBC political editors, the PM argued it would “take away the power of the government… to decide how long it would remain in the EU”.
Speaking to the BBC’s political editor for the South of England, Peter Henley, Mr Johnson said he accepted that he needed to “reach out across the House to get Brexit done”.
“We do need to bring people together, and get this thing done.
“Tempers need to come down, and people need to come together because it’s only by getting Brexit done that you’ll lance the boil, as it were, of the current anxiety and we will be able to get on with the domestic agenda.”
MPs have criticised a number of comments Mr Johnson made during an ill-tempered debate in the House of Commons on Wednesday – the day after the Supreme Court ruled the prorogation of Parliament was unlawful.
Labour MP Paula Sherriff said she had received death threats which often quoted the prime minister’s words, including “surrender act”.
Pointing to a plaque in the chamber commemorating Labour MP Jo Cox, who was murdered by a right-wing extremist days before the EU referendum in 2016, Ms Sherriff said: “We should not resort to using offensive, dangerous or inflammatory language for legislation that we do not like, and we stand here under the shield of our departed friend with many of us in this place subject to death threats and abuse every single day.”
“We must moderate our language, and it has to come from the prime minister first.”
In response, Mr Johnson said: “I have to say, Mr Speaker, I’ve never heard such humbug in all my life.”
The prime minister also later said: “Believe me: the best way to ensure that every parliamentarian is properly safe and to dial down the current anxiety in this country is to get Brexit done.”
Speaking to the BBC political editor for the North West of England, Nina Warhurst, the prime minister said: “I totally deplore any threats to anybody, particularly female MPs, and a lot of work is being done to stop that and give people the security that they need.
“But I do think in the House of Commons it is important I should be able to talk about the surrender bill, the surrender act, in the way that I did.”
He argued the law would “take away the power of this government, and the power of this country to decide how long it would remain in the EU and give that power to the EU and that’s really quite an extraordinary thing”.
When Mr Johnson talks about the “surrender bill”, he is referring to the European Union (Withdrawal) (No. 2) Act, also known as the Benn bill.
The act – which became law earlier this month – stipulates the prime minister will have until 19 October to either pass a deal in Parliament or get MPs to approve a no-deal Brexit.
Once this deadline has passed, he will have to request an extension to the UK’s departure date to 31 January 2020 from the EU.
If the EU responds by proposing a different date, the PM will have two days to accept that proposal. But during this two-day period, MPs – not the government – will have the opportunity to reject the EU’s date.
On Thursday, Labour leader Jeremy Corbyn promised to push his MPs to vote for a general election as soon as a Brexit delay is implemented.
He said: “We will be taking parliamentary action on this again next week to ensure that the prime minister does not crash us out of the EU on October 31 without a deal.”
Meanwhile, Rachel Johnson, the prime minister’s sister, told BBC Radio 4’s World at One that her brother was using the Commons as a “bully pulpit”.
Ms Johnson, who stood for pro-European party Change UK – which has since altered its name to The Independent Group for Change – in June’s European elections, added: “It’s not the brother I see at home. It’s a different person.”
Elsewhere, former Conservative prime minister Sir John Major has criticised Mr Johnson and warned that a “general election would solve nothing” in the Brexit crisis.
Mr Johnson has been calling for an early general election, but under the Fixed-term Parliaments Act he needs the support of two-thirds of MPs. He has twice failed to achieve this.
Speaking to the Centre for European Reform, Sir John said an election “would merely fuel the current feeling of disillusionment and disunity”.
“In the present atmosphere it would be likely to become the most unsavoury election of modern times,” he said.