Cardinal Seán Brady has said he is sorry that he offended people by saying that Bishop John Magee should stay on in Cloyne.
He said he was surprised by reaction to his statement last week.
It follows last month's exposure, by an independent Church Board, of inadequate and sometimes dangerous child protection practises in Bishop Magee's diocese.
Cardinal Brady said that the independent report on Cloyne raised some important issues that must be addressed and this was still the case for the sake of victims.
He explained that he said what he had said in Killarney because Bishop Magee was accepting responsibility and it was important to accept that responsibility.
Cardinal Brady was speaking in Maynooth on his way into a special meeting of the hierarchy to discuss the fallout from the Cloyne controversy on clerical child sexual abuse.
There have been many calls for Bishop Magee's resignation since the report.
Archbishop Diarmuid Martin has said that any of priests who want to minister in Dublin will have to satisfy the archdiocese that they are safe to work with children.
His decision was revealed in a joint statement by the hierarchy following the meeting.
Bishop John Magee apologised victims of abuse, to those working with them and to the general public for the suffering and frustrations occasioned by his diocese's failures.
Earlier this month, Archbishop Martin welcomed Fr Michael Mernagh, one of Bishop Magee's strongest critics, to Dublin's Pro Cathedral.
Today's special meeting was only the third to be held.
Both of the others followed the resignation of Bishop Brendan Comiskey from Ferns for his failure to respond adequately to allegations that clergy had abused young boys.