However, the head of the department since November refused to characterise a one-on-one meeting later month that is now under scrutiny or say whether had had any "negative feedback" from ministers.

Earlier on Wednesday, the Home Affairs Minister was grilled in question time by the Deputy Opposition Leader, Sussan Ley, over a Sky News report that she had reduced Ms Foster to tears last month in an "incredibly robust" discussion over the public release of a document sought by Liberal senator James Paterson. Nine newspapers had also reported that Ms Foster had blindsided Ms O'Neil and Immigration Minister Andrew Giles over the earlier than expected release of the document.

Ms O'Neil had not denied the report, however she insisted she had a "very warm and collaborative relationship" with Ms Foster.

In a spillover estimates hearing late on Wednesday night, Ms Foster confirmed she met the minister and her chief of staff on the day after the document has been released, describing reports of abuse as "absolutely baseless".

"At no point at that occasion, or ever, has minister O'Neill verbally abused me," she told the Opposition's James Paterson as he questioned her.

The secretary described her relationship with both ministers as "very close, very constructive".

The document released to estimates earlier than expected on February 12 had detailed the criminal history of 149 former immigration detainees released after the High Court overturned indefinite immigration detention.

The highly-charged matter continued in Parliament on Wednesday when the Coalition refused to back rushed government legislation that would introduce special ministerial powers over deportations of non-citizens.

Prodded further in the spillover hearing by Senator Paterson, Ms Foster said she was not going to detail private conversations with ministers apart from saying it was a "regular, one-on-one" meeting.

"Ministers' relationships with their secretaries, strong ones like mine are, are based on trust. And I'm not going to discuss the details of the private conversations I have with my ministers," she said.

Senator Paterson then repeated the general warning that it was contempt of the Senate to interfere with a witness in any way.

Ms Foster firmly but calmly pushed back.

"Minister O'Neill has never and I can never imagine her conducting herself in that way," she said.

"Neither minister O'Neill nor minister Giles nor any of their staff have ever attempted to interfere with the way I handle estimates. They are in fact scrupulous in making it clear that the way in which I answer questions and the approach I take to estimates is my call."

The secretary was then asked several times by Greens senator David Shoebridge if she had had any negative feedback from ministers or their offices.

"Senator, I've said quite clearly, I think the issue for me as a public servant is whether or not I am influenced in the way in which I answer questions or approach Senate estimates and the answer is an unequivocal no," she explained.

"The reason I have corrected the record on the issue of verbal abuse is because it was in the media today and it's a very public and relevant issue and it is utterly untrue."

Earlier, Ms O'Neil repeatedly insisted she had an incredibly warm and collaborative relationship with Ms Foster.

"We are doing very important work together cleaning up the catastrophic mess left in Home Affairs by the Leader of the Opposition," she told Parliament.

Ms Foster was appointed to head the department in November after the sacking of Mike Pezzullo.