Two Roman Catholic bishops in Ireland resigned on Christmas day in the wake of a damning investigation into decades of church cover-up of child abuse in the Dublin archdiocese.

Dublin Bishops Eamonn Walsh and Ray Field offered an apology to child-abuse victims as they announced their resignation during Christmas mass. Priests read the statement to worshippers throughout the archdiocese, home to a quarter of Ireland's 4 million Catholics.

Earlier this month two other bishops, Donal Murray of Limerick and Jim Moriarty of Kildare, resigned following the publication on 26 November of a three-year investigation into why so many abusive Dublin priests escaped justice for so long.

The government-ordered investigation found that Dublin church leaders spent decades shielding more than 170 paedophile priests from the law. They began providing information to police only in 1995 – but continued to keep secret, until 2004, many files and other records of reported abuse.

In a joint statement Walsh and Field said they hoped their resignations "may help to bring the peace and reconciliation of Jesus Christ to the victims (and) survivors of child sexual abuse. We again apologise to them."

"Our thoughts and prayers are with those who have so bravely spoken out and those who continue to suffer in silence," the statement said.

The Dublin archdiocese has faced a rising tide of civil lawsuits from abuse victims since the mid-1990s, after one abuse victim, former altar boy Andrew Madden, went public with the church's effort to buy his silence and protect a serving priest. The archdiocese estimates its ultimate bill for settlements and legal costs may top €20m (£18m).

Archbishop Diarmuid Martin, a veteran Vatican diplomat put in charge of Dublin in 2004 with a brief to confront the abuse scandal, had called for his two auxiliary bishops to quit, but both initially refused. Walsh had been a bishop since 1990, Field since 1997.

In his Christmas sermon, Martin said the church for too long placed its self-interest above the rights of its parishioners, particularly innocent children. He said they, as well as the dedicated majority of priests, had been betrayed by their leaders.

"It has been a painful year," he told worshippers at St Mary's pro-Cathedral in Dublin. "But the church today may well be a better and safer place than was the church of 25 years ago – when all looked well, but where deep shadows were kept buried."

In remarks to Dublin's thousands of victims of clerical child abuse, Martin said: "No words of apology will ever be enough for the hurt caused and the way your hurt was brushed aside."

A fifth serving bishop named in the investigation, Martin Drennan of Galway, said he had done nothing wrong and would not resign. The report also criticised five retired bishops, including Dublin Cardinal Desmond Connell, for suppressing information on abuse and preferring to transfer priests to new parishes.

The report also found that senior police officers and other state agencies deferred to church authority until the 1990s – and even referred public complaints about child-molesting priests back to the bishops to handle on their own.