Sir Gavin Williamson has been accused of telling a senior civil servant to "slit your throat" when he was serving as defence secretary.
An ex-official from the Ministry of Defence told The Guardian that Sir Gavin also told them to "jump out of the window" in what they felt was a sustained campaign of bullying.
But in a statement, Sir Gavin said: "I strongly reject this allegation and have enjoyed good working relationships with the many brilliant officials I have worked with across government.
"No specific allegations have ever been brought to my attention."
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The Cabinet Office minister is currently facing allegations that he sent abusive messages to former chief whip Wendy Morton, complaining that he and other colleagues had been excluded from the Queen's funeral for political reasons.
But while Prime Minister Rishi Sunak has condemned the language as "not acceptable", he said it was "right" for a complaints investigation to take place "before making any decisions about the future".
And his official spokesman earlier said the PM had full confidence in him.
According to The Guardian, the civil servant, who later left government, said Sir Gavin "deliberately demeaned and intimidated" them on a regular basis.
While they reported the incidents informally to the MoD's head of human resources, they decided against making a formal complaint.
However, they said a senior military aide working in the department later apologised to them for not calling out his behaviour.
A Cabinet Office spokesman said: "The Cabinet Office has not received notice of any formal complaints about Gavin Williamson's behaviour from his time at the Ministry of Defence or any other department."
Sir Gavin served as defence secretary from November 2017 until May 2019 but was fired by then-PM Theresa May over a row around a leak from government.
He was hired back by Boris Johnson as education secretary two months later, but was again ousted in September 2021 after much criticism of his handling of the brief during the COVID pandemic.
Mr Sunak brought him back into government two weeks ago to serve as a Cabinet Office minister who also attends cabinet.