(CNN) -- The head of the Irish Catholic Church, Cardinal Sean Brady, admitted Wednesday that the church's response to abuse had been "hopelessly inadequate."
"The church must continue to deal with the enormity of the hurt caused by abuse of children by some clergy ... and the hopelessly inadequate response to that abuse in the past," Brady said Wednesday.
Church leaders must "own up to and take responsibility for any mismanagement or cover-up of child abuse," he said.
The cardinal also apologized for his role in the church's investigation into an abusive priest in 1975.
"I want to say to anyone who has been hurt by any failure on my part that I apologize to you with all my heart," he said at St. Patrick's Cathedral in Armagh, Ireland.
"I also apologize to all those who feel I have let them down. Looking back I am ashamed that I have not always upheld the values that I profess and believe in," Brady said, according to a copy of the remarks released by Ireland's Catholic Communications Office.
The deeply Catholic country has been badly shaken by a government-backed report that found the Archdiocese of Dublin and other Catholic Church authorities in Ireland covered up child abuse by priests from 1975 to 2004. Child sexual abuse was widespread then, the report found.
Pope Benedict XVI said Wednesday he has finished writing his official statement, or pastoral letter, on the child abuse scandal facing the Catholic Church in Ireland.
He will sign the letter Friday and send it "soon after," Benedict told the faithful in an address on St. Patrick's Day.
"My hope is that it will help in the process of repentance, healing and renewal," he said.
Brady has been under fire over the investigation into the Rev. Brendan Smyth, one of the country's most notorious child-abusing priests.
Brady's office said Tuesday the cardinal -- then a priest and teacher with a doctorate in canon law -- had been asked to investigate two complaints against Smyth in 1975 but had no decision-making power. He reported his findings to Bishop Francis McKiernan, his office said, and McKiernan recommended Smyth get psychiatric help.
But John Kelly, founder of Irish Survivors of Child Abuse, said Brady should not have remained silent about what he learned in the course of investigating Smyth, who later was convicted of dozens of counts of child abuse in both Northern Ireland and the Irish Republic. Smyth died in prison.
"He's basically using the Nuremberg defense -- he was carrying out orders," Kelly said, in reference to the justification many Nazis used in their war crimes trials after World War II.
There has been particular outrage over the revelation that two boys who filed complaints against Smyth were asked to sign confidentiality statements as part of Brady's investigation.
The oaths of secrecy were "to avoid potential collusion" between the two boys as church officials investigated the case, the Catholic Communications Office said this week.
Despite his criticism of Brady, Kelly said it would not necessarily do any good for the cardinal to resign.
"He's lost all moral authority to lead, but by replacing him, it won't resolve the problem," Kelly said, arguing the Vatican would "just replace guys with other guys."
The best solution, he said, would be for the Roman Catholic Church to let secular authorities deal with accusations of abuse, rather than trying to handle them itself.
"They have to accept secular authority, and they can get on with the business of religion," Kelly said. "It would be in the church's own interest. Resignations in themselves aren't the answer."
Four Irish bishops tendered their resignations in the wake of the government-backed report.
The pope has been under fire since it was revealed a priest suspected of abusing children was allowed to move into his diocese when he was Archbishop Joseph Ratzinger in Germany in 1980.
The Archdiocese of Munich and Freising said in a statement Monday it must have been clear at the time that the priest -- whom multiple sources identified to CNN as Peter Hullermann -- was coming to get therapy for allegedly molesting children. He was convicted of abuse in 1986 after Ratzinger moved to Rome. Hullermann was suspended Monday.
Hundreds of allegations of sexual or physical abuse of children by Catholic clergy have come to light in Germany, Austria and the Netherlands this year
CNN's Frederik Pleitgen in Berlin, Germany, contributed to this report.