Ms O'Neil was targeted by Deputy Opposition Leader Sussan Ley on Wednesday in a highly charged question time after the Coalition earlier thwarted the government's attempt to rush through legislation to remove non-citizens who Australia does not owe obligations to protect.

The minister was grilled over a Sky News report that the secretary was seen leaving the minister's office in tears last month after an "incredibly robust" discussion. Earlier Nine newspapers reported that Ms Foster blindsided the minister and Immigration Minister Andrew Giles over the release of a document, requested by the opposition, detailing the criminal history of 149 former immigration detainees.

Ms Ley asked Ms O'Neil repeatedly whether she verbally abused Ms Foster, but the minister never referred to the February meeting.

"I don't know how many times I will have to repeat this to her," Ms O'Neil told Parliament.

"I have an incredibly warm and collaborative relationship with the secretary of my department. We are doing very important work together cleaning up the catastrophic mess left in Home Affairs by the Leader of the Opposition."

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

The Canberra Times has sought a response from the Department of Home Affairs.

Ms O'Neil insisted all of her answers to Ms Ley were accurate and she praised Ms Foster.

"She is a public servant of decades of standing serving the government. It is why I supported the decision to appoint her to her position and we continue our warm and collaborative relationship," she said.

The opposition's immigration spokesman Dan Tehan said both ministers have questions to answer over their conduct.

"Minister Giles, because in a week when we had 149 detainees, having been released from detention not being properly monitored and a boat arrived off the coast of Western Australia, he wasn't talking to his departmental head, and Minister O'Neil has serious questions to answer about the conduct in that meeting that has been reported. It's over to them," he said.

Greens senator David Shoebridge said senior public servants should not be silenced nor intimidated.

"It should not be so hard to be a public servant in this place and tell the Parliament the truth," he told reporters.

"It shouldn't be career limiting to answer questions honestly and directly.

"The only political careers that should be at risk here are any minister or any member of the Albanese government that's trying to silence the public servants when they're trying to do their job and give Parliament evidence, tell them the truth."