Priti Patel is facing a government investigation into whether she breached ministerial rules following allegations that she bullied staff and briefed against her most senior civil servant.
Boris Johnson has asked the Cabinet Office to “establish the facts” following allegations that the home secretary breached the ministerial code.
“Allegations have been made that the home secretary has breached the ministerial code. The home secretary absolutely rejects these allegations,” Gove said.
“The prime minister has expressed his full confidence in her and having worked closely with the home secretary over a number of years, I have the highest regard for her - she is a superb minister doing a great job.
“This government always takes any complaints relating to the ministerial code seriously, and in line with the process set out in the ministerial code the prime minister has asked the Cabinet Office to establish the facts.”
Under questioning from senior Labour MP Hilary Benn, Gove admitted the inquiry could look into any past complaints about Patel from her time as employment minister or international development secretary.
It comes after reports that a formal complaint was made about Patel when she was employment minister between May 2015 and July 2016.
Benn asked Gove: “Could you tell the House whether any complaints were received by Downing Street in respect of the conduct of the current home secretary when she was the secretary of state for international development and a minister at the department of work and pensions?
“And if so, were they investigated?”
Gove replied: “It is the case that the inquiry that is proceeding will look at all complaints that may have been made, I cannot say more than that.”
On Sunday, Johnson declared his “confidence” in Patel and said she was doing a “fantastic” job.
But Corbyn suggested the PM had spoken prematurely and called for an external lawyer to lead the investigation into the home secretary.
“Why, without a proper investigation, has the prime minister defended the home secretary, calling her fantastic and saying he absolutely has confidence in her?
“A minister in breach of the ministerial code cannot remain in office and should be dismissed.”
The Labour leader added: “Isn’t the truth that this is a government led by bullies, presided over by a part-time prime minister who not only can’t be bothered to turn up but simply won’t take the vital action required when the very integrity and credibility of the government is on the line.”
In a statement on Saturday, Rutnam said “tension” developed in his relationship with Patel after he challenged her over her behaviour.
He said staff had told him that Patel had been “shouting and swearing, belittling people (and) making unreasonable demands”.
Quitting the civil service after 33 years, he accused Patel of lying about her part in a “vicious and orchestrated briefing campaign” against him, and denied counter-briefing against the home secretary.
On Thursday, HuffPost UK revealed that home secretary Priti Patel had wanted to move Andy Tighe, one of her most senior officials, out of the department on Christmas Eve and asked Rutman to deliver the news.
Rutnam refused to do so, believing it too cruel to effectively sack his colleague on Christmas Eve, HuffPost UK understands.
Rutnam’s refusal to carry out Patel’s orders is said to be one of the factors that has led to a breakdown in their relationship.
Relations between the pair were said to have deteriorated to such a level that Patel has blacklisted her permanent secretary’s staff and is cutting them out of regular day-to-day meetings.
Prior to Rutnam’s resignations there had been reports that Patel had demanded his removal.