The prime minister triggered the process after his chief of staff received confidential information from a "primary and direct" source with knowledge of the claims, separate to Ms Higgins herself.

"In response and based on that information, I have asked my chief of staff to commence a process in accordance with advice from the Department of Finance for dealing with complaints against staff members," he told parliament on Thursday.

Ms Higgins has also made a formal complaint to Mr Morrison's chief of staff, asking him to investigate whether anyone in the prime minister's office tried to privately undermine her loved ones.

The former Liberal staffer wrote to John Kunkel after the prime minister suggested nobody from the parliamentary press gallery had raised the accusations with his chief of staff.

Mr Morrison has previously been asked more than a dozen times in the parliament whether he has investigated the allegations.

He was asked again during a radio interview on Thursday whether he could say categorically his office had not engaged in such behaviour.

"Nothing has been raised with my office from anyone in the gallery making any of those accusations or any discomfort about anything that my office has done," he told the ABC.

"People make allegations all the time second, third-hand. But there's no one who has raised that with my chief of staff out of the gallery, no."

Shortly after his comments, Ms Higgins lodged a formal complaint.

"In the days following my interview with The Project regarding my experience in Parliament House, I was made aware by numerous journalists about the backgrounding that was happening to my partner," she wrote to Mr Kunkel.

"To my knowledge, this was being done by staff within the prime minister's media team.

"I believe in giving people the benefit of the doubt. It is entirely plausible the prime minister did not know that this was happening, however the more relevant point is that it did occur."

Ms Higgins said the backgrounding was reported to her personally by "various sources" at news.com.au, The Daily Telegraph and Network 10.

It was also referenced during an ABC radio interview with a Network 10 journalist and subsequently reported by various outlets.

Ms Higgins has also requested to provide evidence to department secretary Phil Gaetjens, who is running an inquiry into which of the prime minister's staff knew of her rape allegations before they were made public.

The investigation has been put on hold while police investigate the rape allegations.

"It is my express desire to present my evidence to Mr Gaetjens at the appropriate time once the review recommences," Ms Higgins wrote.

The furore engulfing the government was sparked by Ms Higgins coming forward alleging she was raped by a colleague in 2019.

There have since been rape accusations levelled at Attorney-General Christian Porter and revelations of a toxic workplace culture inside Parliament House.

Mr Morrison has not made direct contact with Ms Higgins since she went public, nor offered her job back.

The prime minister is also digging in behind Liberal senator Eric Abetz, who is accused of making vulgar comments about Ms Higgins that amounted to victim-blaming.

"Senator Abetz has absolutely denied this completely," he said.

Women across Australia continue to raise reports of inappropriate behaviour with links to politics.

Parliaments in NSW, Queensland, Tasmania and Canberra have each been told of allegations of rape, groping, harassment and slut shaming.

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