The Pope has begged forgiveness from Catholics subjected to sex abuse by members of the clergy.
Pope Francis also apologised for the failure of Church leaders to deal with the issue. He has been meeting with a group of a victims from Ireland, Britain and Germany.
He said the Catholic Church "must weep and make reparation" for what it did to them.
"I feel the gaze of Jesus and I ask for the grace to weep, the grace for the Church to weep and make reparation for her sons and daughters who betrayed their mission, who abused innocent persons" he said.
"Today, I am very grateful to you for having travelled so far to come here".
"I beg your forgiveness, too, for the sins of omission on the part of Church leaders who did not respond adequately to reports of abuse made by family members, as well as by abuse victims themselves" he added.
He also asked the people present to "help me ensure that we develop better policies and procedures in the universal Church for the protection of minors and for the training of church personnel in implementing those policies and procedures".
A total of six people attended the private morning mass at the Pope's Vatican residence earlier before they engaged in talks.
Francis had said he would show zero tolerance for clergy who abused children.
He has already set up a new Child Protection Commission. Its membership includes the Irish campaigner Marie Collins.
The Irish Times religious affairs correspondent Patsy McGarry said earlier that the meeting marked a significant step forward.