Prime Minister Malcolm Turnbull said two weeks ago that Adelaide Archbishop Philip Wilson should have resigned when he was convicted in May of failing to report to police the repeated abuse of two altar boys by a pedophile priest in the Hunter Valley region north of Sydney during the 1970s.
Malcolm Turnbull says Archbishop Wilson's position is untenable.
Turnbull was speaking ahead of a meeting yesterday with senior Catholic officials.
"I am conscious of calls for me to resign and have taken them very seriously", Wilson said earlier this month. "The time has come for the Pope to sack him".
Wilson was sentenced by Magistrate Robert Stone to 12 months' jail on July 3, but will serve the term in home detention and is eligible for parole after six months.
Wilson suffers from diabetes, heart disease, Alzheimer's disease and depression - conditions that would further deteriorate behind bars and "may even threaten his survival", said Mr Temby.
He remains free on bail and will return to court next month to find out whether he will serve his sentence in prison or at his sister's house in home detention.
He was found guilty, in the Newcastle Local Court on May 22, of failing to report allegations of child sexual abuse by convicted paedophile Maitland priest, James Fletcher, dating back to 1976.
Father Frank Brennan, the chief executive of Catholic Social Services, has previously said Wilson had to quit for the good of the church.
The Australian Catholic Bishops Conference did not respond to requests for comment and the church in Adelaide said a statement was not available at this time.
The royal commission - which ran for five years - spoke to thousands of victims and heard claims of abuse involving churches, orphanages, sporting clubs, youth groups and schools.
The key witness in the landmark trial said he trusted Wilson would take action after being told of the abuse which occurred when Mr Creigh was 10 years old in 1971. He died in jail of a stroke in January 2006. "It places other people at risk", he said.