Prime Minister Malcolm Turnbull has called on the Pope to sack Adelaide Archbishop Philip Wilson.
The 67-year-old Catholic cleric was sentenced to 12 months in jail earlier this month for concealing child sexual abuse, but he plans to appeal.
"He should have resigned, and the time has come for the Pope to sack him," Mr Turnbull told reporters in Sydney on Thursday.
Opposition Leader Bill Shorten backed the PM, describing Wilson's position as "untenable".
"If he doesn't have the decency to resign then his superiors in the church should take action," Fairfax media reported Mr Shorten as saying.
"The community has spoken. The courts have spoken. Now it's time for the Church to truly listen."
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 PM's call came just before he was due to head into a meeting with Sydney Archbishop Anthony Fisher, Australian Catholic Bishops Conference president and Brisbane Archbishop Mark Coleridge and the incoming Archbishop of Melbourne, Peter Comensoli.
A number of bishops have privately counselled Wilson to resign since his conviction, with Archbishop Comensoli going on the record last week.
He said Wilson's refusal to resign had led to a "terrible impasse".
"Philip Wilson has chosen to not offer his resignation, and has rightly said he has a right to appeal, which he has done," he told the ABC's Religion Report.
"But in all of that, there remains what is good for the people of God in this circumstance, and most particularly, what would be good for the people of the Archdiocese of Adelaide.
"For those reasons I think the path he is taking is not of benefit for God's people in Adelaide, so I along with a number of other bishops have sought to counsel Philip in that regard."
Wilson was found guilty in May of failing to report to police the historical sexual abuse of two altar boys by a pedophile priest after a landmark magistrate-only trial in Newcastle Local Court.
Calls for his resignation in the wake of the guilty verdict came thick and fast, but Wilson said he would only resign if his appeal in the NSW District Court was unsuccessful.
He stepped aside from all official duties, with Pope Francis last month appointing Bishop Greg O'Kelly as the Apostolic Administrator of the Archdiocese of Adelaide in what was regarded as direct involvement in the case from the Vatican.
"The Pope's intention is to provide stability for the people of the Archdiocese during these challenging times," Bishop O'Kelly said at the time.
The Australian Catholic Bishops Conference also reaffirmed last month that only the Pope could compel a bishop to resign.
Australian Associated Press