The pope has accepted the resignation of Philip Wilson as archbishop of Adelaide after he was convicted of concealing child abuse, in a further sign of the Vatican’s struggle to keep on top of a series of scandals.

In May, Wilson became the most senior Catholic cleric to be convicted of not disclosing to police abuse by another priest. He failed to report the abuse of two altar boys by James Fletcher, a paedophile priest, in the 1970s.

The archbishop was sentenced to 12 months in prison on 3 July and ordered to serve a minimum of six months. He immediately launched an appeal against the conviction.

Despite calls for his resignation from many quarters, Wilson insisted he would not step aside until his legal options were exhausted. However, in a brief statement released at midday in Rome, the Vatican announced the Pope had accepted Wilson’s resignation.

The Australian Catholic Bishops’ Conference also issued a statement on the decision. Wilson’s resignation was the “next chapter in a heartbreaking story of people who were sexually abused”, it said, adding that the move “may bring some comfort to them, despite the ongoing pain they bear”.

The pope’s decision is the latest in a string of child abuse issues he has been forced to address in recent months.

At the weekend, Francis accepted the resignation of the US cleric Theodore McCarrick as cardinal after allegations of sexual abuse, including claims involving an 11-year-old boy.

Two dioceses in New Jersey secretly reached financial settlements in 2005 and 2007 with men who said they were abused by McCarrick decades ago, according to a New York Times report.

Last month, the pope accepted the resignation of Juan Barros, a Chilean bishop who the pontiff robustly defended in January despite claims of a cover-up of clerical sexual abuse. Francis accepted the resignation of four other Chilean bishops over scandal.

In April, he admitted he had made “grave errors” of judgment regarding Barros, and invited Chilean abuse victims to Rome to beg their forgiveness.

Next month, the pope is to visit Ireland, where he will be expected to meet survivors of clerical sexual abuse and publicly address a scandal that has caused irrevocable damage to the Catholic church over recent decades.

The Australian prime minister, Malcolm Turnbull, who took the highly unusual step of publicly calling on the pope to remove Wilson, welcomed his resignation, saying it belatedly recognised the many calls for him to resign as archbishop of Adelaide.

Turnbull added: “There is no more important responsibility for community and church leaders than the protection of children.”

In a statement released on Monday, Wilson said: “I made this decision because I have become increasingly worried at the growing level of hurt that my recent conviction has caused within the community.

“I had hoped to defer this decision until after the appeal process had been completed. However, there is just too much pain and distress being caused by my maintaining the office of archbishop of Adelaide, especially to the victims of [James] Fletcher.”

Wilson’s appeal is to continue, the Catholic bishops conference said. It added that his resignation may bring some comfort to Fletcher’s victims “despite the ongoing pain they bear”.

Wilson, 67, maintains his innocence. His legal team made four attempts to have the case thrown out, arguing their client has Alzheimer’s and should therefore avoid trial.

Wilson had showed “no remorse or contrition”, according to Robert Stone, the magistrate who sentenced him.

In August, the court will assess whether Wilson can serve his sentence under home detention.