Sussan Ley calls on Katy Gallagher, Labor ministers to outline involvement in Brittany Higgins case

But the Greens leader Adam Bandt has called the controversy "disgusting" and sends the wrong message to women.

Ms Ley claims Senator Gallagher's alleged foreknowledge of the alleged sexual assault case, outlined in published excerpts of text messages in The Australian between Ms Higgins and her partner David Sharaz, could mean that she has misled Parliament.

The opposition claims Senator Gallagher had potentially misled Parliament when she said in Senate estimates in June 2021 that "No-one had any knowledge. How dare you?" when it was put to her that Labor figures knew about the allegations regarding Ms Higgins before they became public.

Mr Sharaz, in the newly revealed text messages timed four days before the first stories emerged about Ms Higgins' alleged assault, boasts of a special relationship with Senator Gallagher, and said to Ms Higgins that "she's really invested now ha ha" in the matter.

Senior Labor figures, such as the Prime Minister and the Deputy Prime Minister Richard Marles, have denied the ACT senator and minister has misled Parliament, while Mr Albanese has declared he has "absolute confidence" in her.

"If it is the case that any politician was tipped off about this serious allegation, and then sought to obtain political advantage from it, I can't see how they could remain a minister, let alone a minister for women," Ms Ley said.

"We've only heard one side of the story through these text messages. But that's because the other side, the Finance Minister, refuses to front up and take questions.

"All of them need to front up and be unequivocal in outlining what knowledge or involvement they had, and when, especially before the story was made public."

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The criminal case was aborted earlier this year and charges were dropped against the accused man, Bruce Lehrmann, who maintains his innocence.

Senator Gallagher was last interviewed on Wednesday, when she told the ABC: "My statements are all on the record, and I'm comfortable with those."

The Canberra Times has again sought comment from the minister, but she has not been available.

Mr Albanese has labelled any idea of a conspiracy as "nonsense" and pushed back on Liberal party outrage over a controversy that erupted while the Coalition was in power.

"Take a step back, Kochie, what is being suggested here by Peter Dutton," the Prime Minister told Sunrise.

"You had allegations by a Liberal staffer that another Liberal staffer had a sexual assault in a Liberal minister's office and, somehow, Katy Gallagher has some responsibility for what was going on here?

"This is bizarre."

Asked "Did your colleague mislead Parliament?", the Prime Minister came back with a firm "No".

Assistant minister Jenny McAllister told Sky News Australia Senator Gallagher's statement that she's comfortable with her public responses and her public statements is "the end of it from my perspective".

Mr Bandt said the political mudslinging over Brittany Higgins is "disgusting" and "sends the wrong message to every woman" who are thinking about coming forward with complaints.

"Women should be able to come forward without worrying that their text messages will be splashed across the media," he said.

"Nothing we have seen so far suggests the need for an inquiry or referral to the NACC (the new National Anti-Corruption Commission)."