The cardinal urged more victims to speak out
In a letter read out at church services on Sunday, Cardinal Desmond Connell, whose handling of the issue has been widely criticised, praised the courage of victims who have spoken out about clerical abuse.
More than 20 Catholic priests, brothers and nuns have been convicted of sexually abusing children in Ireland in the past 10 years.
The cardinal urged other victims to speak out, saying the church needed to know the full scale of the problem to be able to respond fully.
He said those coming forward had often done so "in the face of quite inadequate responses on the part of the Church".
And he expressed deep regret for instances where this had been the case in his own archdiocese.
'Courage and perseverance'
"Only those who have suffered this terrible outrage can fully understand what is involved in revisiting what was done to them and exposing the trauma over again in the glare of publicity," the letter continued.
"We are so much in their debt for the courage and perseverance they have shown in doing this," it said.
Thirty bishops from the Republic of Ireland and Northern Ireland held an emergency general meeting last week to discuss the issue.
The meeting followed the resignation of the Bishop of Ferns, Brendan Comiskey, in the face of criticism of his handling of complaints of abuse in his diocese.
International scandal
Similar scandals have emerged in other countries - particularly the United States - and last month Pope John Paul made his first public denunciation of guilty priests.
In the US on Sunday, the leader of the Los Angeles archdiocese said he "took responsibility" for making a "mistake" in transferring a priest to work in a hospital without telling the institution the man was alleged to have abused children.
In an interview with the Los Angeles Times, Cardinal Roger Mahony said he should have forced Father Michael Wempe to resign when he heard of the accusations.
On Friday, the head of the Boston archdiocese, Cardinal Bernard Law, refused to bow to pressure to resign over the case at the heart of the sex scandal that has rocked the Roman Catholic Church in America.
Cardinal Law, 70, has been heavily criticised since former priest John Geoghan was convicted of child molesting.
He has acknowledged that he transferred Geoghan to another parish despite knowing of sexual misconduct allegations against the now-defrocked Boston priest.