As Pope Francis opened a four-day conference on Thursday to address the issue of sex abuse in the Catholic clergy, one of the church’s most senior figures was accused of failing to act when incidents of abuse were called to his attention.

Indian cardinal Oswald Gracias, the Archbishop of Mumbai, is himself due to open the second day of the summit in Rome with a conversation about accountability in the church.

He was also among a group of church leaders who met with abuse survivors in a two-hour meeting on Wednesday night, to hear their personal accounts and inputs on the eve of the conference.

Cardinal Gracias was forced to admit he did not call the police immediately when a family came to him in 2015 saying their son had returned from Mass saying he was raped by a parish priest.

A BBC investigation found the cardinal left for Rome that night without alerting the authorities, and only later phoned his bishop to discuss the matter and be told the family had already gone to the police themselves.

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In doing so, Cardinal Gracias may have broken Indian laws protecting children from abuse. Specifically, the regulations require the head of any company or institution to report a possible offence committed by a subordinate under his or her control.

The incident was one of two cases where families expressed dissatisfaction with the cardinal’s response to allegations. In the other, a priest was able to continue offering prayer retreats despite a woman coming forward with claims that he sexually abused her during one of them.

At the time of the 2015 incident, the cardinal was president of the Catholic Bishop's Conference of India and Federation of Asian Bishops' Conferences. And aside from the key roles he is playing at this week’s summit, Cardinal Gracias has been repeatedly tipped as a possible contender to be the next pope.

Asked if he regretted not immediately calling the police over the 2015 allegations, Cardinal Gracias told the BBC: "You know I'm being honest, I'm not 100% sure… but I must reflect on that. I admit whether immediately, the police should have got involved, sure." He described the second set of claims, from 2009, as a "complicated case". The Independent has approached the Archdiocese of Bombay for comment.

It comes as the survivors at Wednesday’s round-table meeting demanded transparency, zero tolerance for abuse and accountability for religious superiors who cover up for rapists at Pope Francis’s high-stakes summit.

They have demanded the church adopt a zero-tolerance approach across the board, with the US bishops' conference considering a model where any priest found guilty of molesting a child would be permanently removed from ministry.

Jamaican survivor Denise Buchanan, who attended Wednesday's meeting, asked “what is the holdup in implementing zero tolerance?”. She said: "It is like, 'Oh, we already have the laws, we just need to implement the laws.' Obviously, the laws are not working because children are being raped right now.”

Though survivors were disappointed that he did not attend the meeting himself, Pope Francis called in his opening remarks on Thursday for the summit to find "concrete and efficient measures" and not simply more condemnations.

"Faced with the scourge of sexual abuse committed by men of the Church against minors, I wanted to reach out to you," Francis told the assembled bishops and heads of religious orders, asking them to "listen to the cry of the little ones who are seeking justice."

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Some victims' groups said the conference was merely meant to cleanse the image of the 1.3 billion-member Church tainted by child rape and molestation by priests, and cover-ups by Church authorities.

But Anne Barrett-Doyle of bishopaccountablity.org, which tracks abuse cases around the world, said she was pleasantly surprised by the pope's opening remarks.

"They said this was going to just a teaching session but he is now talking about concrete measures. That's good but let's see how it ends up," she told the Reuters news agency.

Archbishop Charles Scicluna of Malta, the Vatican's top sexual abuse investigator, said the church had to look at how priests and bishops are appointed.

"The question of future screening of candidates for the priesthood is fundamental," he said in a speech steeped in legal details about how bishops must collaborate with civil authorities, adopting a "culture of disclosure" and for society to know that "we mean business".