Prime Minister Scott Morrison has offered to meet Brittany Higgins anywhere she chooses, should she wish to talk.

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

However, he conceded Ms Higgins was yet to express an interest in meeting him.

“I understand why and that’s fine,” Mr Morrison said 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.”

On Thursday night, Mr Morrison told Channel Nine’s A Current Affair that he doubted Ms Higgins would wish to discuss something “as deeply private and personal” with him as her alleged rape in Parliament House.

Ms Higgins’ claim of her alleged rape in the office of Senator Linda Reynolds and the lack of support she experienced afterwards had triggered “one of the most hard and deeply personal, confronting conversations I have seen take place here”, Mr Morrison told ACA interviewer Tracy Grimshaw.

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Mr Morrison said he often heard statistics about violence against women but Ms Higgins’ story had taken him “deeper into this issue” that he had appreciated before.

“We have gone way deeper, we have gone beyond the sheer shock of violent acts. We are starting to deal with some home truths,” he said.

The Prime Minister defended himself against the accusation that he is late to the issue of sexism, saying that while women “live with it every day”, he has had different experiences.

“For many Australians, this has been like a big wake-up call and it’s been like a red light to say ‘stop, look, listen’, and that’s what we’re doing,” he said.

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But Mr Morrison dug in his heels on his defence of Attorney-General Christian Porter, again labelling him “an innocent man” and rejecting the idea that he could instigate a non-criminal inquiry into a historical rape allegation about him.

He said that “many things … will make our country stronger to deal with these issues”, including the need for respect towards women.

“Equally, our courts, our police, our justice systems, they are also important. We can’t dismiss that and think we are fixing that problem,” he said.

He repeatedly drew an analogy to former opposition leader Bill Shorten, who faced his own rape allegation. Police declined to prosecute the matter.

“That’s not the first time this has happened in this country,” Mr Morrison said.

He called for greater respect in Australian society, including on how people disagree “on this type of issue”.

Mr Morrison is pondering a cabinet reshuffle to try to clear the air after weeks of parliamentary scandals and shocking allegations. On Thursday, he said Mr Porter and Senator Reynolds – who is on medical leave after calling Ms Higgins a “lying cow” – would “continue to play a very important role” in his cabinet.

He declined to say what positions they might serve in, and when a reshuffle would be announced.

Mr Morrison said he had instigated an inquiry into whether his office was backgrounding journalists against Ms Higgins’ family and that he would not condone that conduct.

He told A Current Affair his chief of staff had spoken to a “direct and confidential source” on Thursday, who had allegedly witnessed the backgrounding.

-with AAP