Archbishop Diarmuid Martin has said no apology will ever be sufficient to make amends to those who had been abused by members of the clergy.
"This is the diocese in which I was born," Dr Martin told a news conference at his residence in Dublin. "How do I feel when I have to unveil here before you the revolting stories of the sexual assault and rape of many young children and teenagers by priests of the archdiocese?
"No words of apology will ever be sufficient," he said, with tears in his eyes.
"Excuses, denials and minimisations were taken from abusers. Decisions were taken that resulted in more children being abused. As Archbishop of Dublin, and as Diarmuid Martin a person, I offer to each and every survivor my apology, my sorrow and shame for what happened."
The Archbishop of Armagh and primate of All Ireland, Cardinal Seán Brady, said he was "shocked and ashamed" by the abuse of children described in the report.
"I want to apologise to all those who have been hurt and their families. I also want to apologise to all the people of Ireland that this abuse was covered up and that the reputation of the Church was put before the safety and well-being of children," he said.
Dr Brady said the Catholic Church's current policy of child safeguarding in Ireland puts the welfare of the child "as the paramount concern".
"No one is above the law in this country. Every Catholic should comply fully with their obligations to the civil law and cooperate with the Gardai in the reporting and investigation of any crime," he said.