An anonymous letter sent to Mr Morrison, Labor foreign affairs spokeswoman Penny Wong and Greens senator Sarah Hanson-Young alleges a current cabinet minister raped a woman in 1988, a claim briefly investigated by NSW Police before the complainant asked for the inquiry to be dropped and later died.
Mr Turnbull, who said he was contacted by the victim in December 2019, said the accused minister should come forward and publicly address the allegation.
“The fact is, he owes it to his colleagues and the country to step out, to step forward and say right I’m the person referred to, and then set out all the details,” he told ABC radio.
Mr Turnbull has also called for a coronial inquiry into the woman’s death.
“He should provide a comprehensive statement of what he knows about the allegations. If he’s vigorously denied them to the Prime Minister, he should vigorously deny them to the public,” he said.
“He should describe when he knew the woman, how he knew the woman, what dealings he had with the woman after the events.”
Mr Turnbull said it was “vitally important” the accused minister addressed what he knew about the complaint and when he was made aware of it.
On Monday, Mr Morrison said the minister should not have to stand aside because allegations had been raised in the media. He said he had raised the allegations with the Australian Federal Police. There are, however, growing doubts police will be able to investigate because the woman who alleged the rape died in June.
Mr Turnbull said it was “not good enough” for Mr Morrison to say it was a matter for the police.
“The Prime Minister cannot outsource his responsibility for composing his ministry to the police.
“We are seriously going to have a question time where the opposition asks every single minister whether they are the person named in the complaint,” he said.