VATICAN CITY — Cardinals attending Pope Francis’ summit on preventing clergy sex abuse called Friday for a new culture of accountability in the Catholic Church to punish bishops and religious superiors when they fail to protect their flocks from predator priests.

On the second day of Francis’ extraordinary gathering of Catholic leaders, the focus of debate shifted to how church leaders must acknowledge that decades of their own cover-up, secrecy and fear of scandal had only worsened the crisis.

“We must repent, and do so together, collegially, because along the way we have failed,” said Mumbai Cardinal Oswald Gracias. “We need to seek pardon.”

Chicago Cardinal Blase Cupich told the 190 bishops and religious superiors that new legal procedures were needed to both report and investigate superiors when they are accused of misconduct or negligence in handling abuse cases.

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He said lay experts must be involved at every step of the process, since rank-and-file Catholics know far better than priests what trauma abuse and cover-up has caused.

“In large part it is the witness of the laity, especially mothers and fathers with great love for the church, who have pointed out movingly and forcefully how gravely incompatible the commission, cover-up and toleration of clergy sexual abuse is with the very meaning and essence of the church,” he said.

“Mothers and fathers have called us to account, for they simply cannot comprehend how we as bishops and religious superiors have often been blinded to the scope and damage of sexual abuse of minors,” he said.

Francis summoned 190 bishops and religious superiors for the four-day tutorial on preventing abuse and protecting children after the scandal erupted again last year in Chile and the U.S. While the Vatican for two decades has tried to crack down on the abusers themselves, it has largely given the bishops and superiors who moved them around from parish to parish a pass.

Mothers and fathers have called us to account.

Cupich called for transparent new structures of reporting allegations against superiors, investigating them and establishing clear procedures to remove them from office if they are guilty of a grave negligence in handling cases.

He proposed that metropolitan bishops — who are responsible for other bishops in their geographic area — should be tasked with conducting the investigations, with the help of lay experts. The metropolitan bishop would then forward the results to the Vatican.

It wasn’t immediately clear how Cupich’s proposals squared with those being studied by the U.S. Conference of Catholic Bishops at large.

Those procedures, which called for a code of conduct for bishops and a third-party confidential reporting system, ran into legal snags last year at the Vatican, which blocked U.S. bishops from voting on them at their November assembly.

At the time of the blocked vote, Cupich proposed his “Metropolitan model,” which on Friday he articulated from the privileged position as an organizer of Francis’ summit. Among the participants in the summit is the head of the U.S. conference, Cardinal Daniel DiNardo, who had been responsible for pushing the proposals blocked by the Holy See.

More than 30 years after the scandal first erupted in Ireland and Australia, and 20 years after it hit the U.S., bishops and Catholic officials in many parts of Europe, Latin America, Africa and Asia still either deny that clergy sex abuse exists in their regions or play down the problem.

Francis, the first Latin American pope, called the summit after he himself botched a well-known sex abuse cover-up case in Chile last year.

Gracias, the Indian cardinal, opened the session by saying bishops must hold themselves accountable and work together to address the problem because it is not confined to a particular region. He told the conference that it is not acceptable for bishops in Africa or Asia to say that the problem of clergy sex abuse doesn’t exist in their regions.

“I dare say there are cases all over the world, also in Asia also in Africa,” Gracias said.