“It is all slander,” Francis said in remarks that immediately caused an outcry. Francis, startled by the response, then sent two investigators, Archbishop Charles Scicluna and Msgr. Jordi Bertomeu, to Chile to examine how church officials had handled sexual abuse reports.

The Vatican investigators issued a 2,300-page report based on 64 interviews, accusing Chilean church leaders of failing to investigate credible allegations. They found that priests who had been accused of wrongdoing were shuttled to new parishes, in some instances putting them in regular contact with minors.

The report said that church leaders went as far as destroying documents.

Francis apologized, admitting he had made “serious errors of judgment and perception of the situation.” In April, he met with three men who had been abused as teenagers, and the next month he summoned the entire Chilean Bishops Conference to Rome. It was there that all 34 bishops offered their resignations.

“I believe Pope Francis realized the social and political challenges facing the church in today’s world, and is pushing the Chilean church toward a crisis from which he is confident something new will arise,” said Mr. Murillo, who was one of the men invited to the Vatican. He now leads the Foundation for Trust, a group for abuse victims.

The pope has accepted the resignations of Bishop Barros and four others. Among them was Alejandro Goic, who led the church’s National Council for Abuse Prevention and has been questioned by prosecutors on accusations that he failed to act on repeated reports of abuse in his own diocese.

Archbishop Scicluna and Monsignor Bertomeu returned to Chile in June to meet with prosecutors and church leaders to follow up on the accusations. The pope’s envoys heard from additional victims and, before leaving, appointed a group of lay people and clergy to continue receiving reports of abuse.