Prime Minister Scott Morrison has again ruled out calling an independent inquiry into rape allegations against Attorney-General Christian Porter.

Mr Morrison argues the allegations should be dealt with through the police and the courts.

“I see no justification for any extra-judicial inquiry that might be set up by a prime minister or any other politician,” he told a business summit on Tuesday.

“We have competent and authorised agencies to deal with these matters both through the police and the courts and that is where I will make my assessments of those matters. That is where it should be done.”

Former cabinet minister Julie Bishop has said the next logical step in the scandal is an inquest led by the South Australian coroner.

Mr Porter is on leave after vehemently denying he raped the woman more than 30 years ago.

The woman who made the claim took her own life in 2020 after telling NSW Police she did not want to proceed with her complaint.

While Labor and some of the woman’s friends have backed calls for an independent inquiry into the allegations, Ms Bishop said an inquest was appropriate.

“It’s within the criminal justice system. There are checks and balances and there are statutory powers,” she told the ABC.

“It has legal standing. And so, that is the next step and I understand from media reporting that’s what the family would welcome.”

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Federal minister Anne Ruston also backed an inquest, but said it was up to the coroner to make an independent decision.

“I think everybody will be happy if the coroner in South Australia decides to investigate,” she said.

Mr Morrison is open to a coronial inquest.

“If there should be coronial inquiries, then that of course is the process and I am happy to see those processes proceed as coroners see fit,” he said.

Former prime minister Malcolm Turnbull said an independent inquiry would be in the best interest of Mr Porter.

“That would enable there to be a process which would enable the issue to be resolved. The problem is it remains unresolved in the minds of many people,” Mr Turnbull said.

The alleged rape of Brittany Higgins in the ministerial office of Linda Reynolds, shortly before a federal election was called in 2019, has also led to pressure for broader reform of political culture.

Ms Bishop said the parliament needed a formal staff induction program and an independent complaints system.

“There’s a powerful culture within all political parties to toe the line, don’t rock the boat, don’t do anything that would damage the party’s prospects,” she said.

“Paradoxically, it can mean a culture develops whereby those who are prone to inappropriate or unprofessional or even illegal behaviour get a sense of protection.”

Treasurer Josh Frydenberg said Ms Bishop had the last laugh against party colleagues who tried to stymie her career.

“She became Australia’s first female foreign minister and did an outstanding job in that role,” he told Sky News.

“She became deputy leader of the Liberal Party – a position I am very privileged to hold right now as her successor.

“She made a big difference in public life, so she has very much had the last laugh when it comes to her career or any attempts by people to stymie it.”

-with AAP