Health Secretary Matt Hancock has defended Priti Patel as “courteous” following bullying claims.
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”.
The home secretary has not publicly responded to Sir Philip’s claims but previously denied she mistreated staff.
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.
But Andrew Marr Show, Mr Hancock described Ms Patel as “very determined” but also “extremely courteous”.
He added that she was “probably closer to where the public are on the issues of law and order than any home secretary in recent history”.
Labour leadership contenders have also commented on Sir Philip’s departure, with Rebecca Long-Bailey calling it “an example of this Tory government in disarray” and Lisa Nandy saying the Home Office was “in chaos”.
Shadow chancellor John McDonnell said the situation was “unprecedented” and suggested that Ms Patel was “on the way out”.
And the former head of the civil service, Lord Kerslake, argued that the home secretary might 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.
European Union and UK agreed to their ‘red lines’ ahead of talks
He said “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.”
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 Sir Philip’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.
UK finance chief quits amid reports of clash with Boris Johnson
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.
Health Secretary defends Priti Patel over bullying claim made by the ex-top civil servant in her department.