Prime Minister Malcolm Turnbull is calling on Pope Francis to fire Adelaide Archbishop Philip Wilson, who is appealing his conviction of charges of covering-up sexual abuse committed by clergy members.

"As far as Philip Wilson is concerned, he should have resigned, he should have resigned and the time has come for the pope to sack him," PM Turnbull said.  "There are many leaders that have called on him to resign, it is clear that he should resign and I think the time has come now for the ultimate authority in the church to take action and sack him."

It has been almost two months since a court convicted Archbishop Wilson of covering up abuse by priest Jim Fletcher in the NSW Hunter region during the 1970s.  He was sentenced to twelve months detention, but would be eligible for parole after just six months.  Wilson says he has the right to take his case to a higher court. 

"Since that process is not yet complete, I do not intend to resign at this time," he said last week, "However, if I am unsuccessful in my appeal, I will immediately offer my resignation to the Holy See."

South Australia officials have also called on Wilson to stand down, as has opposition leader Bill Shorten.