The family of a woman who accused Attorney-General Christian Porter of a historical rape have thrown their support behind holding an inquiry into the circumstances of her death.
Prime Minister Scott Morrison rejected calls to launch an independent inquiry into the sexual assault accusations against the nation's top law officer.
Mr Porter emphatically denies the allegations he raped the woman in 1988 when he was 17 and she was 16.
Lawyers acting for the family said they would be open to a coronial inquest or independent investigation into her death.
"They are supportive of any inquiry which would potentially shed light on the circumstances surrounding the deceased's passing," the lawyers told News Corp.
Mr Morrison is under increasing pressure to take further action despite trying to draw a line under the allegations.
Labor has backed either a coronial or independent inquiry to restore faith in cabinet.
"It's time for the prime minister to give both himself and Australians confidence that Mr Porter is a fit and proper person to hold the office of attorney-general," Opposition Leader Anthony Albanese told reporters in Perth.
"This cannot be the end of the matter."
The prime minister has stressed the importance of respecting the rule of law after NSW Police closed an investigation because of a lack of admissible evidence.
He 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," Mr Morrison told reporters in NSW.
"That's not how we run the rule of law in Australia."
The South Australian woman went to NSW police last year but withdrew her complaint citing medical and personal reasons before taking her own life in June.
The attorney-general is expected to be on leave for about two weeks but won't quit cabinet after vehemently denying the allegations.
The Greens and some independent MPs support a judicial probe.
Tasmanian senator Jacqui Lambie said if the public confidence in Mr 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.
She criticised the prime minister for not reading a dossier detailing the allegations that she and Greens senator Sarah Hanson-Young sent him.
Mr Morrison said he was briefed about the documents after they were passed on 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 the ABC.
The woman's lawyer Michael Bradley has consistently called for an independent inquiry into the matter.
Mr Porter on Wednesday identified himself as the cabinet minister accused of the alleged sexual assault.
"It just didn't happen," he told reporters.
Nationals MP Barnaby Joyce also backs 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.
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Australian Associated Press