"There is now a dark cloud over the cabinet and the government," Mr Bandt said on Sunday.

More details are emerging about the historical rape allegation made against a senior member of the government, also reported to be a member of cabinet. An anonymous letter detailing the allegation, asking the prime minister to investigate, was sent to Mr Morrison last week. Attached to the letter was a statement by the alleged victim, a woman who died by suicide in June last year.

It was also sent to Labor senator Penny Wong and Greens Senator Sarah Hanson-Young, both of whom have forwarded the letter to the Australian Federal Police.

On Saturday, Finance Minister Simon Birmingham said the matter should be left to police, as did Health Minister Greg Hunt on Sunday.

Before her death, the woman involved had spoken to NSW Police, as the incident was alleged to have happened in Sydney. It has been reported she told police she did not want to continue with an investigation before her death.

NSW Police confirmed the investigation was suspended after the alleged victim's death, and would not be reopened.

"The circumstances of this case and the potential difficulties of prosecuting the matter mean the Prime Minister cannot wait for the police investigation alone," Mr Bandt said, calling for Mr Morrison to call his own investigation.

"If the prime minister doesn't at least stand this man aside while he conducts his own inquiry, then he's sending the terrible message there is space in his Cabinet for someone with an unresolved rape accusation."

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Labor leader Anthony Albanese said it was appropriate for the allegation to be investigated by police, but said Mr Morrison must confirm to himself the minister involved should stay in his job.

"We need to make sure that these are serious allegations, that they are investigated appropriately, and that these issues aren't politically managed," he told the ABC's Insiders program.

He didn't commit to calling for an independent investigation of the allegations or for the minister to stand aside.

"This is a moment whereby Australians will be looking for, after what has been a very difficult fortnight, common decency to shine through here, and for an appropriate response that isn't about political management, that is about transparency, is about making sure that processes are respected. But then, I think, people will be looking for a resolution," he said.

Former prime minister Malcolm Turnbull has called for a coronial inquiry into the death of the woman.

Mr Turnbull has also revealed the woman wrote to him in 2019 with details of the allegations and he had since passed that correspondence to the South Australian police.

Speaking at a Writers' Week event in Adelaide on Sunday, Mr Turnbull revealed the woman had written to him and his wife Lucy in December 2019 seeking their advice.

"She described a pretty horrific rape that she said had occurred at the hands of this person, a person she said is now in the Cabinet," Mr Turnbull said.

"One of the things she noted, I might say, is that she'd kept extensive diaries. She mentioned that she had a lawyer and was talking to the NSW Police."

Mr Turnbull wrote back expressing sympathy and concern for her and told her she was doing the right thing in going to police.

The former PM said after learning of the woman's death in South Australia in the middle of last year it struck him there would likely be an inquest.

"I got in touch with the police commissioner here and I sent him the correspondence she sent us and our reply," Mr Turnbull said.

"I don't know whether there will be an inquest or not. Frankly, there should be. The allegation is incredibly serious. In the circumstances, a woman who has got a complaint ongoing about a senior public figure, taking her own life.

"There clearly needs to be some form of inquest."

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