Pope Francis ended his visit to the US tonight with a homily that emphasised the importance of faith in God to help families cope with the challenges of the modern world. Earlier, he met adult victims of child sex abuse and repeated his commitment that their abusers must face justice.

Pope Francis, addressing hundreds of thousands of the faithful at a Mass marking the end of the World Meeting of Families in Philadelphia, said Jesus had spoken strong words against causing scandal. "For Jesus, the truly intolerable scandal consists in everything that breaks down and destroys our trust in the working of the Spirit."

Jesus encountered hostility from people who did not accept what he said and did, the Pope added.

"The temptation to be scandalised by the freedom of God, who sends rain on the righteous and the unrighteous alike, bypassing bureaucracy, officialdom and inner circles, threatens the authenticity of faith."

Urging adults to take care both of  their grandparents and their children, he said: "Anyone who wants to bring into this world a family which teaches children to be excited by every gesture aimed at overcoming evil, a family which shows that the Spirit is alive and at work, will encounter our gratitude and our appreciation. Whatever the family, people, region, or religion to which they belong. May God grant to all of us, as the Lord's disciples, the grace to be worthy of this purity of heart which is not scandalized by the Gospel."

He criticised "sterile divisions" which be said could no longer be accommodated.

"The urgent challenge of protecting our home includes the effort to bring the entire human family together in the pursuit of a sustainable and integral development, for we know that things can change."

He also warned of the "dangerous temptation", going so far as to describe it as a "perversion", to think the spirit cannot work in the lives of non Catholics.

"To raise doubts about the working of the Spirit, to give the impression that it cannot take place in those who are not part of our group, who are not like us, is a dangerous temptation. Not only does it block conversion to the faith; it is a perversion of faith. Faith opens a window to the presence and working of the spirit. It shows us that, like happiness, holiness is always tied to little gestures."

Before Mass he met three women and two men who as children had been victims of sex abuse by clergy or by members of their families or their teachers. "I hold the stories and the suffering and the sorry of children who were sexually abused by priests deep in my heart," he said. "I remain overwhelmed with shame that men entrusted with the tender care of children violated these little ones and caused grievous harm. I am profoundly sorry. God weeps."

He added: "The crimes and sins of the sexual abuse of children must no longer be held in secret. I pledge the zealous vigilance of the church to protect children and the promise of accountability for all."

Pope Francis has met victims in Rome but this was the first time he had met victims outside Italy. He has been criticised by survivors during this visit for not doing enough to address the scandal.

Also at the meeting was Cardinal Seán Patrick O'Malley, Archbishop of Boston and chair of a commission set up by the pope to protect minors.

In Washington he commended the "courage" of bishops and commended them for helping bring healing to victims. In New York he told clergy that many had to "bear the shame of some of your brothers who harmed and scandalized the church". The tone of these remarks prompted the Survivors Network of those Abused by Priests to criticise him as a  "throwback". The group said: "He talks and acts like the church hierarchy is the real victim in this crisis."