A Liberal senator and backbencher have called for an inquiry into how Brittany Higgins’ private messages became public.

Andrew Bragg said the emergence of the messages – which were published in The Australian and across other News Corp publications last week – needed to be investigated properly to stop a repeat of such an incident.

“I expect that there will be a proper investigation because, I mean, why would anyone come forward with allegations of assault if this is the result?” Senator Bragg told ABC Radio on Wednesday.

He was later joined by backbench MP Bridget Archer, who said she’d support an inquiry.

“It is important to realise it is a challenging and sensitive issue for people involved and also for victims and survivors observing,” Ms Archer told The Guardian, in reference to how the issue is being discussed in parliament.

The push for an inquiry came a day after Attorney-General Mark Dreyfus confirmed the Australian Federal Police are investigating the unauthorised leak of court material provided under subpoena.

The leaked text messages suggest then-opposition senator Katy Gallagher knew of Ms Higgins’ rape allegations before they were made public in the media in February 2021.

The Coalition says there is a case to be made that the now-finance minister misled a Senate estimates hearing in 2021 about her knowledge of the allegations.

In the upper house on Tuesday, Senator Gallagher said her comments two years ago were about the broader question of “whether I was involved in that matter becoming public”.

“And I was not,” she said.

She did not deny being informed that Ms Higgins was preparing to go public, but said she kept the confidence and did not act on the information.

Ms Higgins alleges she was raped by then-fellow Liberal staffer Bruce Lehrmann inside the Parliament House office of then-minister Linda Reynolds in 2019, a claim he has always denied.

Senator Bragg said the way the debate over the matter was unfolding in the Senate was “very, very ugly”.

“This whole thing has been a tawdry affair and it is hugely regrettable how it’s played out publicly,” he said.

His comments came amid more questions about the report commissioned by then PM Scott Morrison into who knew about Ms Higgins’ accusations, and when.

Led by then head of the Department of Prime Minister and Cabinet, Phil Gaetjens, it was ordered in the days after Ms Higgins went public with her allegations.

It was paused, at the request of the AFP, due to the pending criminal trial. It has never been restarted.

Government frontbencher Jenny McAllister said there were questions about the report for the Coalition.

“I think that it is appropriate that the former government answer questions about the way that review was conducted and why its findings were never released,” she said.

On Wednesday, deputy opposition leader Sussan Ley said the investigation was put on hold on AFP advice, and legal inquiries into the Higgins case were continuing – specifically the ACT’s independent board of inquiry that is investigation Mr Lehrmann’s prosecution.

“The questions that we want answered are simple questions that relate to recent information that has come to light,” she said.

“Where are senior ministers of this Labor government, who are running a mile from the questions that the Australian people have a right to get answers to?”

The political fallout from the matter continues to escalate as Liberal senator Linda Reynolds threatens to take defamation action against Environment Minister Tanya Plibersek in relation to a television interview that discussed the alleged rape.

Ms Plibersek confirmed she had received an “interesting letter” on Tuesday.

“As far as I’m concerned, all legal options are on the table,” she said.

The Australian reported Senator Reynolds issued a defamation concerns notice to Ms Plibersek over an interview that aired on Monday in which the Labor minister was accused of wrongly implying the former Liberal frontbencher covered up the rape allegations.

Ms Higgins and Mr Lehrmann both worked for Senator Reynolds at the time of the alleged incident.

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– with AAP