In a pastoral letter read out at church services throughout his diocese on Sunday, the Archbishop of Dublin, Cardinal Desmond Connell, said the Church's failure to deal more compassionately with victims was due to a lack of understanding rather than neglect.
More than 20 Catholic priests, brothers and nuns have been convicted of sexually abusing children in Ireland in the past 10 years.
"Incalculable harm has been done to those who were abused," his letter said.
"Further scandal has undoubtedly been caused by the fact that, having approached the church in expectation of the best possible care and the most sympathetic response, some people suffered further hurt."
The cardinal also pointed to the level of media coverage given to the issue, which he said had "undoubtedly contributed" to the process of coming to terms with the nature and scale of the problem.
Similar scandals have emerged in other countries - particularly the United States - and earlier this year, Pope John Paul made his first public denunciation of guilty priests.
Cardinal Connell's letter also pointed to the the slow response of the church in understanding the trauma victims suffered, and said it "had not always responded as quickly or appropriately as it should have done.
"I want to apologise again from my heart for the terrible betrayal they have suffered," he said.
Child protection service
"I do so in my own name, with a keen sense of our failures to deal more adequately with the problem, as well as in the name of all of us who in any way represent the church."
He added: "I deeply regret the mistakes I have made in seeking to come to grips with the problem."
The cardinal referred to the Diocesan Advisory Panel, which was set up in April 1996 to make recommendations to him about what action was appropriate in each case, and said he had accepted its recommendations in every instance.
He added that on the advice of the panel of five men and five women he had authorised the establishment of a Child Protection Service in the diocese, details of which were to be published.
Cardinal Connell also urged anybody in the diocese who had been abused to report what happened to the police.