Home Secretary Priti Patel is facing pressure to respond to bullying allegations made by the former top civil servant in her department.
Sir Philip Rutnam, the Home Office’s most senior official, resigned on Saturday citing a “vicious and orchestrated” campaign against him.
Labour’s Sir Keir Starmer said Ms Patel must come to Parliament to “explain”.
Ms Patel, who has not publicly responded to Sir Philip’s claims, previously denied she mistreated staff.
Health Secretary Matt Hancock defended the home secretary, telling Sky News she was “very determined but also very courteous”.
In his statement, Sir Philip said he received allegations that Ms Patel’s conduct towards employees included “swearing, belittling people, making unreasonable and repeated demands”.
He said he now intended to take legal action against the Home Office on the basis of constructive dismissal.
Ms Patel, who has rejected newspaper reports about the claims, did not publicly comment on Sir Philip’s statement.
Labour leadership contender Sir Keir said: “The home secretary has a duty to come to Parliament on Monday to explain the allegations made about her own conduct.”
He also called for the head of the civil service, Cabinet Secretary Mark Sedwill, to start “an immediate investigation” into the circumstances surrounding Sir Philip’s departure.
“There are now urgent questions that must be answered and steps that need to be taken,” he added.
Meanwhile, shadow Cabinet Office minister Jon Trickett called on the prime minister himself to make a statement.
And the former head of the civil service, Lord Kerslake, suggested that the home secretary would have to resign if Sir Philip wins his legal action.
Lord Kerslake said the resignation – and the way in which Sir Philip left – was “extraordinary”, adding that it will send “shockwaves” through most of the civil service.
Lord Kerslake told BBC Breakfast on Sunday: “Every institution can do better and that’s true for the civil service as well, but what you don’t do is go to war with the civil service.”
According to BBC correspondent Iain Watson, allies of Ms Patel are privately suggesting that Sir Philip was not up to the demands of the job.
The Home Office has to deliver on two key election pledges – recruiting more police officers and swiftly introducing a new, post-Brexit immigration system.
Asked if the prime minister had full confidence in Ms Patel, a Downing Street source said Mr Johnson had full confidence in his cabinet.
Sir Mark thanked Sir Philip for his “long and dedicated career of public service” and said he received the resignation “with great regret”.
He said Shona Dunn, who had been Mr Rutnam’s deputy, will become acting permanent secretary.
Sir Philip’s departure, and the manner of it, goes way beyond any normal policy problems or clashes.
He took aim not just at Priti Patel, but alluded to what he said was a “wider pattern” in government.
Add this to the resignation of Sajid Javid, the former chancellor who expressed concerns about how the government is behaving, there is mounting evidence of unhappiness with how Prime Minister Boris Johnson and his team are running things.
Certainly it is a government in a hurry, willing to rattle cages in order to get things done.
But governments who want to get things done need an effective civil service to make things happen. A very public breakdown in trust like this does not help that cause.
Indications at this early stage are that Ms Patel’s position is secure. But with an employment tribunal in the offing, pressure may well build in the coming weeks.
If Sir Philip pursues his case as he says he will, exactly what happened behind closed doors may soon be out there for all to see.
Read more from Laura here.