SYDNEY - Australia's Prime Minister Scott Morrison is facing growing pressure over his handling of a series of alleged sexual assaults involving staff of his ruling Coalition, including an alleged rape by a Cabinet member.

Despite enjoying soaring popularity due to his handling of the Covid-19 pandemic, Mr Morrison is now engulfed in a serious crisis that is raising questions about his political judgment.

The crisis began when a former political adviser, Ms Brittany Higgins, claimed she was sexually assaulted in Parliament by a fellow adviser in the office of a minister in 2019.

Although she reported the alleged rape to the police, she decided not to proceed with the complaint, citing concerns about the impact on her job. Ms Higgins was then adviser to the defence minister, Ms Linda Reynolds.

The 26-year-old, who has reportedly now made a formal police complaint, said she believed the government had been concerned about the potential political fallout rather than her own welfare.

Following her decision to speak out, four other women have come forward with claims that they were also sexually assaulted by the same adviser. The adviser, who has not been named, was sacked following the incident with Ms Higgins because he had breached security by entering the ministerial office after hours.

Mr Morrison apologised for the way the government handled the incident and has ordered separate reviews of the handling of complaints and workplace standards in Parliament and the protection of staff.

But the troubles for the Prime Minister have since worsened following the airing of fresh claims about an alleged rape by a Cabinet minister of a 16-year-old girl.

The incident allegedly occurred in 1988 before the minister entered politics. The victim had contacted police in 2019 and also reportedly prepared a detailed document about the incident, but took her own life last June.

Neither the woman nor the minister has been named, though the minister's identity is widely known.

New South Wales Police said on Tuesday that the investigation into the incident had been closed and that the woman's alleged statement could not serve as formal evidence.

"Based on information provided to NSW Police, there is insufficient admissible evidence to proceed," police said in a statement.

Mr Morrison said earlier this week that the minister has denied the rape allegation and should not have to step aside due to media reports of allegations.

But critics say that Mr Morrison should order an investigation into the allegation and that the minister should admit to being the accused person and potentially stand aside.

The minister is expected to declare himself on Wednesday (March 3) and make a public statement in which he will insist on his innocence, according to media reports on Tuesday.

Former prime minister Malcolm Turnbull said on Tuesday that the minister should name himself and provide an explanation to the public. He said Mr Morrison's insistence that the allegation was merely a matter for police was "not good enough".

"If the minister had vigorously denied the claims to the Prime Minister, he should also deny them to the public," he told ABC Radio.

"The fact is he owes it to his colleagues and the country to step out, step forward to say, right, 'I'm the person referred to' and then set out all the details."

The Labor opposition party also called on the Prime Minister to order an investigation.

"There is a dark cloud now over the government," said Labor leader Anthony Albanese.

"The idea that this can just be allowed to drift and just stay where it is, is in my view untenable."

However, some commentators expressed sympathy for the minister, saying that he was being subjected to a "show trial" and was not being afforded a presumption of innocence.

"His career in politics will be over because there is nothing he can say that will placate his accusers," wrote political commentator Chris Uhlmann in The Sydney Morning Herald on Tuesday.