Dr Brady said he would be travelling to the Vatican with Archbishop of Dublin Diarmuid Martin to discuss the findings of the report with Pope Benedict.
Dr Brady said it was only fair that time should be given to bishops to hear their side of the situation "before prescribing remedies".
Speaking on RTÉ today, the Catholic Primate of all Ireland said the church would be working closely with the Minister for Children Barry Andrews “to ensure that the church observes the highest standards of child safeguarding in every area”.
He said the church hierarchy was anxious to implement the best possible standards as soon as possible. "This cannot be put on the long finger," he said.
He said Bishop of Limerick Donal Murray "was considering his position" and would make a statement presently. "I'm confident that Bishop Donal will do the right thing," he said.
Dr Martin has said he was not satisfied with the response of some of the bishops named in the Dublin diocesan report.
Dr Brady said the Dublin archbishop has written to the bishops and auxiliaries criticised in the report asking that they offer explanations for the commission's findings.
"Perhaps we should wait and see what those replies are," the Cardinal said. "I think it's only fair that we should wait to hear their side of the situation before prescribing remedies."
Asked what he would do if it were found that children had been abused as a result of any failing on his part, Dr Brady said he would stand down.
“I would remember that the abuse of children is a very serious crime in civil and canon law. It’s also a very grave sin,” he said. "If I found myself in a situation where I was aware that my failure to act had allowed or meant other children were abused, well then I think I would resign."
Asked about the calls for further inquiries, Dr Brady said the welfare of survivors of abuse had to be taken into consideration and what was best for child protection throughout the State - for which he said the State had primary responsibility.
"Whatever is best for child protecting, bring it on. We hope that what were are doing at the moment is best for protecting - in other words, training people up and down our parishes . . . to ensure people know their responsibilities . . . that children will be safe at all times."
He said the Church's child protection policies had to be known, implemented, and audited.
"That's the way we will give accountability and win back the confidence of people that we are sincere about this and determined that whatever it takes to safeguard children will be done."
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