Sir Gavin Williamson could face a cabinet office investigation over bullying reports, Downing Street hinted on Tuesday.
It has been alleged that the minister told a senior civil servant to “slit your throat”.
He made the remarks in front of colleagues during a meeting when he was Defence Secretary, according to a report in the Guardian.
On another occasion told the civil servant to “jump out of the window”.
Sir Gavin, now a Cabinet Office minister, has denied the allegations.
He is also being probed over damning emails he sent to then Chief Whip Wendy Morton during Liz Truss’ 50-day administration.
The Prime Minister’s official spokesman said on Tuesday that Rishi Sunak still has confidence in Sir Gavin, but is considering whether any action should be taken over the “serious allegations”.
He said: “Obviously, there have been further allegations reported this morning.
“Those are serious allegations that have come in. It’s true that no formal complaint has been made.”
Downing Street added that it would consider “proper processes” before commenting further.
It comes as Sir Gavin was told on Tuesday that “we are all sackable” as he faced a fresh claim of alleged bullying.
Work and Pensions Secretary Mel Stride defended Sir Gavin as an “important member” of Rishi Sunak’s Cabinet.
“To be fair to to Gavin he has apologised and recognised that while he may have been frustrated at the time, it was inapproriate,” Mr Stride told Sky News.
But pressed whether he was sackable, he added: “I don’t think anybody is unsackable.
“As we have seen in the recent past even the Prime Minister is sackable.
“We are all sackable at some point, depending on the circumstances.”
Mr Stride said any decision on Sir Gavin’s future should be taken after the results of an investigation into his conduct.
He added that Mr Sunak has known there had been a “disagreement” between he and Ms Morton but did not know the substance of the allegations.
He stressed that it was “unacceptable to adopt that kind of language and tone” as used by Sir Gavin to the former Chief Whip in his emails.
In a series of expletive-laden texts exposed over the weekend, Sir Gavin accused Ms Morton of seeking to "punish" MPs out of favour with then-premier Ms Truss by excluding them from the Queen's funeral, warning: "There is a price for everything."
