Dominic Raab has refused to comment on the bullying allegations surrounding him, saying it would be “improper”.
The justice secretary was repeatedly asked about the investigation into his conduct.
Independent lawyer Adam Tolley KC is looking into a number of formal complaints made by civil servants against Raab.
Sky News confronted him with allegations from individuals across various government departments who raised concerns about his treatment of colleagues.
However, Raab said: “I’ve said I would co-operate fully with the inquiry. I’m not going to comment on anonymous sources in the media.
“In fact it is a breach of the rules of the inquiry for anyone to do so and of course I want to respect that.”
Asked whether he recognised some of the behaviour he had been accused of by anonymous sources, Raab replied: “It is actually improper for me to comment on the question you have just asked, it is a breach of the rules of the inquiry…As a matter of professional integrity, I’m not going to do that.”
Pressed on his relationship with civil servants, he added: “Of course you want to have a positive relationship. With the vast majority of people that I do, that is the case. But I’m not going to comment on the allegations or the claims.”
Raab has previously vowed to quit Rishi Sunak’s Cabinet if he is found guilty of bullying staff.
However, he refused to step down ahead of the investigation into his behaviour, saying “innocent until proven guilty”.
Staff from multiple departments he has led have made complaints about his behaviour – including at the Brexit department, foreign office and ministry of justice.
Former Tory chair Jake Berry has called on Raab to step aside from his ministerial roles while he is investigated over the claims.
Sunak has resisted calls for Raab to be suspended or to step aside while he is investigated, with the prime minister instead waiting for the inquiry to conclude.
Raab has previously said he is not a bully and always “behaved professionally” towards staff.
According to the Daily Telegraph, Boris Johnson privately warned Raab about his conduct while he was in Number 10.