Morrison said a further investigation would undermine democracy and cast doubts over the competence of police.

“There is not the mob process. There is not the tribe-has-spoken process. That’s not how we run the rule of law in Australia,” the prime minister told reporters in NSW on Thursday.

The South Australian woman went to NSW police last year but withdrew her complaint before taking her own life in June.

Calls for an inquiry have been centred on a retired judge or eminent lawyer conducting a thorough investigation.

Porter has publicly rejected he sexually assaulted a woman in 1988 when he was 17 and she was 16.

An emotional Porter on Wednesday identified himself as the cabinet minister accused of the alleged sexual assault.

“It just didn’t happen,” he told reporters.

“Could I have forgotten or misconstrued the things that I have read, which are said to have occurred? Absolutely not.”

The attorney-general is expected to be on leave for about two weeks but won’t quit cabinet after vehemently denying the allegations.

The opposition, the Greens and independent MPs are calling for an inquiry to restore faith in cabinet.

Tasmanian senator Jacqui Lambie said if the public confidence in Porter did not rebound he would be forced to resign.

“You just cannot have an attorney sitting there where the public has lost all confidence in him whether he’s guilty or not,” the independent told Sky News.

Labor frontbencher Penny Wong said the allegations against the attorney-general were serious and credible.

“The prime minister really needs to stop looking at this as an issue of glib political management,” she told ABC radio.

Senator Wong criticised the prime minister for not reading a dossier detailing the allegations that she and Greens senator Sarah Hanson-Young sent him.

Morrison said he was briefed about the documents after they were sent to federal police.

Greens senator Larissa Waters said there was no possible advantage for women in making up sexual assault allegations.

“His statement was based on the premise that he thinks women make this sort of stuff up and I just simply don’t accept that,” she told ABC TV.

The woman’s lawyer Michael Bradley has consistently called for an independent inquiry into the matter.

Nationals MP Barnaby Joyce has also backed an external inquiry to stop ongoing speculation about the allegations.

SA coroner David Whittle has asked the state’s police to further investigate the death.

Police had provided the coroner with a case file on Monday, but Mr Whittle found the investigation to be incomplete.

The government has been under the pump for weeks after former Liberal staffer Brittany Higgins alleged she was raped by a colleague at parliament house.

Morrison said new staff counselling arrangements were in place with the Finance Department no longer delivering support.

He said the terms for a multi-party inquiry into parliamentary culture would soon be finalised.

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