On the Pope's behalf, the cardinal asked forgiveness from "those who have been harmed by priests and bishops, whose actions – and inactions – gravely harmed the lives of children entrusted to their care."
He admitted that "carrying the cross" of discipleship is "a costly grace and often we fall down on the job."
"We want to be part of a Church that puts survivors, the victims of abuse first, ahead of self-interest, reputation and institutional needs," Cardinal O'Malley said.
"We have no doubt of Jesus' compassion and love for the survivors even when they feel unloved, rejected, or disgraced. Our desire is that our Church reflect that love and concern for the survivors of sexual abuse and their families and be tireless in assuring the protection of children in our Church and in society."
He said he has encountered much suffering during his visits with victims.
The "tragic evil of sexual abuse of minors" has caused "profound distress," resulting in addictions, damaged relationships, the suffering of families and even suicide, he said.
"The wounds carried in Ireland as a result of this evil are deep and remind us of the wounds of the body of Christ," he said.
"But today, through the saving power of the cross, we come together to share in each other's sorrows as well as our collective hope for the future," he told the penance service. "We come together to bind up the wounds we carry as a result of this crisis and to join in prayer for healing, reconciliation and renewed unity."
Cardinal O'Malley said he sees a "window of opportunity" to build a "holier Church" in response to the crisis.
Sunday's ceremony, he said, "gives testimony to the longing of so many to rebuild and renew this Archdiocese and the Church throughout Ireland."
"Just as the Irish people persevered and preserved the faith when it was endangered, and carried it to many other countries, the commitment to sustain the faith provides the opportunity for the hard lessons of the crisis to benefit the Church in our quest to do penance for the sins of the past and to do everything possible to protect children in the present and in the future."
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The cardinal and a team of assistants are now carrying out their second visit to the archdiocese to interview victims and collect accounts for a report to the Vatican, due by Easter.
The other three "visitators" to Irish archdioceses have conducted similar penitential services in recent months.
Archbishop Thomas Collins of Toronto's office told CNA that he has completed his interviews in the Archdiocese of Cashel and Emly and will also be submitting his report to the Pope by Easter.
Cardinal Cormac Murphy-O'Connor of Westminster, England has concluded his visits of the Archdiocese of Armagh. Archbishop Terrence Prendergast of Ottawa will complete his second round of visits to the Archdiocese of Tuam from March 5-12.
Archbishop Timothy Dolan of New York completed visits of the Pontifical Irish College seminary in Rome and the major seminary at Maynooth, Ireland early this month. His office said he will be submitting his report by April 1.
A spokesperson for Archbishop Dolan said that after interviewing 113 Irish seminarians, "he sees much hope for the renewal of the faith in Ireland."