Scott Morrison said he was happy to meet with the former Liberal staffer, who alleges she was raped by a colleague inside a ministerial office.

He said Higgins had not expressed an interest in meeting with him up to this point.

“I understand why and that’s fine,” Morrison told reporters on Friday.

“We’ve always sought to respect her privacy and her wishes on this and I could also appreciate why she wouldn’t necessarily meet in Parliament House, that would be totally understandable.

“We can arrange to meet in other cities.”

The prime minister has instigated an inquiry into whether his office was briefing journalists against Higgins’ partner in an attempt to discredit and undermine her.

His chief of staff has spoken to a “direct and primary” source who witnessed the alleged backgrounding.

He thanked the confidential informant for coming forward but would not say when any action would be taken.

“With anything as sensitive as this, it’s important it follows a proper process to look into these matters,” Morrison said.

“It’s not appropriate for me to give a running commentary on each step of that process.

“Australians should know that we are taking this extremely seriously and following up on all of that information that has been provided to us.”

Labor asked every day for two weeks whether the prime minister’s staff had backgrounded against Higgins’ loved ones.

Opposition Leader Anthony Albanese said it was disappointing Morrison took action only after somebody came forward with first-hand information, rather than seeking out an answer himself.

Higgins also wrote to the prime minister’s chief of staff requesting an investigation, saying the backgrounding was reported to her by various sources at multiple media outlets.

“He should ask his office and just say what happened with the undermining of Brittany Higgins’ loved ones,” Albanese said.

The prime minister is seeking a circuit-breaker after being criticised for his tone-deaf response to a national debate about the treatment of women.

The conversation was sparked by Higgins coming forward last month to allege she was raped by a colleague in 2019.

There have since been rape accusations levelled at Attorney-General Christian Porter, which he denies, and revelations of a toxic workplace culture in Parliament House.

The horrific allegations have engulfed the Morrison government and started a wider debate about sexual discrimination, harassment and abuse.

The prime minister has admitted repeatedly failing in his tin-eared response to the national movement and conceded he failed to grasp the depth of anger about violence against women.

He has also admitted people in his government failed Ms Higgins after she reported the alleged rape in parliament.

Morrison will try to clear the air by reshuffling his frontbench line-up in coming days.

But shifting Porter and Defence Minister Linda Reynolds, who had to apologise for calling Higgins a “lying cow”, to other portfolios is unlikely to satisfy those demanding accountability.