Cardinal Brady has said he will stay on as the Archbishop of Armagh.
He had been facing increasing pressure to resign after he participated in an investigation into clerical abuse.
It was revealed in March that the Cardinal was present when children signed vows of silence over allegations against a paedophile priest in 1975.
Dr Brady also revealed he has asked a Vatican inspection of child protection procedures to include a visit to the Armagh diocese.
His comments follow the publication of the Annual Report of the National Board for Safeguarding Children in the Catholic Church in Ireland.
It found that nearly 200 new allegations of abuse have been reported to the Catholic Church’s child protection watchdog since April 2009.
In a statement, Cardinal Brady said he was committed with all his "human weaknesses to walk this journey of renewal and to discern God’s will for the Church at this time".
Dr Brady said the impact on abuse survivors of the "drip-by-drip revelation of past failings has to be addressed".
The Archbishop revealed he had held both public and private meetings with survivors of abuse.
"I also listened to people from the Diocese, in Parishes and in Diocesan groups."
Cardinal Brady said he was committed to building on the substantial progress made in child safeguarding in recent years and to achieve the objectives set out by Pope Benedict XVI in his pastoral letter to Irish Catholics.
He has also asked Pope Benedict for an additional bishop in the diocese.
Cardinal Brady said that he would be appointing a Director of Child Safeguarding for the diocese who would handle all future allegations of child abuse and report to civil authorities in both jurisdictions.
Sharing ‘soft information’
"In the future, it will be this statutory authority and not the Church (or any other organisation which works with children in Northern Ireland) that will decide who is permitted to work with children," he said.
" As part of our registration with this new Independent Safeguarding Authority, Bishops in Northern Ireland will give a commitment to sharing ‘soft information’ held or known about any person working in a Church context, as well as all allegations of abuse, with the new Authority."
The head of Ireland’s Catholics apologised in March for his role in mishandling the case of a serial child abuser.
As a priest in 1975 Cardinal Sean Brady was at meetings where children signed vows of silence over complaints against paedophile priest Fr Brendan Smyth.
The Catholic Church in Ireland released more details about why Cardinal Brady asked two victims, aged 10 and 14, to sign secrecy agreements.
The church said the boys were asked to sign oaths "to avoid potential collusion" in evidence-gathering for an internal church inquiry.
It added this this would ensure that the complaints could "withstand challenge."
The church statement did not explain why either Cardinal Brady or his superiors at the time did not share their information with the police. Fr Smyth went on to abuse more children in the following years.
This article is from the BBC News website. © British Broadcasting Corporation, The BBC is not responsible for the content of external internet sites.