Australian prime minister Scott Morrison is standing by an unnamed cabinet minister against calls for him to step down from office over an allegation that he raped a 16-year-old girl more than 30 years ago.

The allegation has cast a cloud over the 16 men in Mr Morrison's 22-minister cabinet and feeds complaints of a culture within parliament that is toxic for women.

The allegation was contained in an anonymous letter sent to the prime minister's office and to three female legislators last week.

The letter contained a statement from a complainant that detailed her allegation of a rape she said occurred in New South Wales state in 1988.

The woman, who has not been publicly named, reported the allegation to police before taking her own life in June at the age of 49.

Morrison said the unnamed cabinet minister "vigorously and completely denied the allegations".

The prime minister said he forwarded the letter to police and discussed the allegation with the federal police commissioner. Mr Morrison said he did not intend to take any further action.

"We can't have a situation where the mere making of an allegation and that being publicized through the media is grounds for ... governments to stand people down simply on the basis of that," Mr Morrison said.

Australia's ministerial code of conduct states a "minister should stand aside if that minister becomes the subject of an official investigation of alleged illegal or improper conduct".

Some within the government argue that because the complainant is dead, her allegation is no longer under official police investigation because a conviction is unlikely.

Senator Sarah Hanson-Young, a Greens party member who received the anonymous letter, said the minister must step down pending an independent investigation by a former judge.

"It is just not right to suggest that this type of allegation could linger, hang over the heads of the entire cabinet," she said.

"Sitting around that table erodes the trust, the integrity and belief that this government takes sexual assault seriously."

Marque Lawyers' managing partner Michael Bradley, who represented the complainant when she took her accusation to police, said the allegation cannot be resolved through the criminal justice system because she had died.

The minister should step down while some independent inquiry investigates the evidence, Mr Bradley said.

"His position is pretty clearly untenable and he should step aside or be stood aside until this matter can be addressed and resolved," he added.

The disclosure comes two weeks after Mr Morrison apologised in parliament to a former government staffer who alleged she was raped by a more senior colleague in a minister's office two years ago.

Brittany Higgins quit her job in January and reactivated her complaint to police after initially not pursuing the case because she felt it would have affected her employment.

The colleague, who has not been named publicly, was fired for breaching security by taking Ms Higgins into a minister's office following a night of heavy drinking.

Three other women have made sexual misconduct allegations against the same man since Ms Higgins went public with her complaint.

A government employee who alleged he raped her last year told The Weekend Australian newspaper the attack would not have happened if the government had supported Ms Higgins' initial complaint.

Mr Morrison responded to Ms Higgins' public complaints by appointing government legislator Celia Hammond to work with political parties to investigate parliament house culture, improve workplace standards and to protect staff.

Ms Hammond and opposition Labour Party senator Penny Wong also received anonymous letters about the 1988 rape allegation.

Ms Wong said she met the complainant in 2019 and the complainant detailed her allegation against the man, who was not in parliament in 1988.

"I facilitated her referral to rape support services and confirmed she was being supported in reporting the matter to NSW Police," Ms Wong said.

Mr Morrison said that before he was told of the rape allegation last week, he had heard "rumours" that an Australian Broadcasting Corp (ABC) investigative reporter was "making some inquiries" around November last year when the ABC's Four Corners programme broadcast its Inside The Canberra Bubble investigation.

The programme accused the ruling conservative Liberal Party of tolerating and condoning inappropriate sexual behaviour.

The program exposed an extramarital affair between population minister Alan Tudge and a female adviser in 2017. It also alleged attorney general Christian Porter had been witnessed "cuddling and kissing" a female staffer in a Canberra bar, which he denies.

The government has condemned the programme.

Communications minister Paul Fletcher has asked the ABC board to explain how the programme was in the public interest and complied with the state-owned broadcaster's obligation to produce accurate and impartial journalism.