The Catholic Primate Cardinal Séan Brady said today he "will reflect on what he has heard from those who have been hurt by abuse".
In his St Patrick's Day homily at Armagh Cathedral this morning, Dr Brady said he was "ashamed" by the fact that he has not always upheld the values that he professes and which he believes in.
There have been calls on the cardinal to consider his position after it emerged at the weekend that he had conducted canonical inquiries into allegations of child sex abuse by Fr Brendan Smyth 35 years ago, involving two young people, without reporting the allegations to civil authorities.
Speaking today, the cardinal apologised again to victims of clerical child sex abuse.
"This week a painful episode from my own past has come before me. I have listened to reaction from people to my role in events thirty five years ago," he said.
"I want to say to anyone who has been hurt by any failure on my part that I apologise to you with all my heart. I also apologise to all those who feel I have let them down. Looking back I am ashamed that I have not always upheld the values that I profess and believe in," he added.
In his homily the cardinal said there was a need to take responsibilty for any mismangement or cover-up of child abuse.
"We must humbly continue to deal with the enormity of the hurt caused by abuse of children by some clergy and religious and the hopelessly inadequate response to that abuse in the past," said Dr Brady.
"For the sake of survivors, for the sake of all the Catholic faithful as well as the religious and priests of this country, we have to stop the drip, drip, drip of revelations of failure," he added.
"Be certain that I will be reflecting carefully as we enter into Holy Week, Easter and Pentecost. I will use this time to pray, to reflect on the Word of God and to discern the will of the Holy Spirit. I will reflect on what I have heard from those who have been hurt by abuse. I will also talk to people, priests, religious and to those I know and love," he added.
Andrew Madden, who in 1995 became the first in Ireland to go public with an abuse lawsuit against the church, dismissed the latest comments from Cardinal Brady.
“The notion of careful reflection is nonsense — he’s had 35 years to reflect on what he did then,” said Mr Madden.
“If the Catholic Church in Ireland is to be led by a man who accurately reflects it in its current state, then maybe it’s only right and fitting that it should be led by a man who has covered up the sexual abuse of children by a priest.
“He’s either going to go or he’s not going to go and if he doesn’t, the Catholic Church can’t pretend to be serious in any way about the issue of child protection and about reaching out to people who have been abused.”
Another abuse survivor and campaigner, Christine Buckley, said: "I still think that Cardinal Brady should do the honourable thing and resign.
"The apology, while it's welcome, isn't enough at this stage. He's head of the Catholic Church in Ireland and he's shown no leadership in this regard because he knew about this for 35 years."
Elsewhere, the Norbertine Order, of which Fr Smyth was a member, issued a statement tonight in which it expressed sadness at the controversy and again acknowledged its failure to remove the paedophile priest permanently from the exercise of ministry.
"The actions taken by the late bishop McKiernan in 1975 were necessitated by our failures. Based on the information provided by Fr Brady, who clearly believed those who he had interviewed, bishop McKiernan prohibited Fr Smyth from exercising ministry in the diocese of Kilmore," the order said.
Speaking in Washington this morning, where he was attending St Patrick's Day festivities, Northern Ireland Deputy First Minister Martin McGuinness became the latest person to say he believed Cardinal Brady should consider his position.
Mr McGuinness described the revelations as "a very grave situation for the Catholic Church".
Making his first comments about the weekend's revelations last night, the Archbishop of Dublin Diarmuid Martin said people want the truth to come out about clerical child sex abuse in Ireland and it may be necessary to extend the remit of the Murphy commission to ensure this is done.
However, he said he would not be calling for the resignation of Dr Brady as this was a personal decision.
“I’ve always said it is not my job to tell people to resign or tell people to stay. I’ve never done that. People should be accountable, render an account of what they have done. Resignations are a personal matter," he said.
Meanwhile, Taoiseach Brian Cowen has rejected suggestions that he is at odds with his Cabinet colleague Green Party leader John Gormley over the handling of the clerical child sexual abuse crisis.
Speaking to journalists in Washington yesterday, Mr Cowen said: “It’s a matter for me to indicate my own views in relation to these situations. There is no discrepancy. The State’s position is that there is equality before the law.”
He was commenting after Mr Gormley said that he would have no difficulty with gardaí investigating the circumstances in which two children were asked to sign oaths of secrecy during the church inquiry into the Smyth case in 1975.
Additional reporting: PA