The Bishop of Limerick Donal Murray has today "humbly apologised" to those who were abused as children as the Vatican confirmed his resignation had been accepted by Pope Benedict.

The bishop addressed churchgoers at Mass at St John's Cathedral in Limerick. In a statement, Bishop Murray said he had heard the views of many survivors, especially in the days following the publication of the Murphy report.

"Some expressed the wish that I should resign; others asked me not to do so. I know full well that my resignation cannot undo the pain that survivors of abuse have suffered in the past and continue to suffer each day. I humbly apologise once again to all who were abused as little children. To all survivors of abuse I repeat that my primary concern is to assist in every way that I can, on their journey towards finding closure and serenity."

The bishop said he had asked the Pope to allow him resign and to appoint a new bishop to the diocese because "I believe that my presence will create difficulties for some of the survivors who must have first place in our thoughts and prayers.

“Let my last words as Bishop of Limerick be those I spoke in St. Joseph's on 29th November last: ‘We are people who believe that God’s mercy and God’s healing are without limit. We are meant to be bearers of that hope to one another and especially to people whose trust was betrayed when they were just little children and who endured the terror, helplessness and suffering inflicted by a frightening and dominant adult. They should always have a special place in our prayers’."

Calls were made for a criminal investigation into how Bishop Murray handled abuse allegations against Fr Thomas Naughton, convicted for child sex abuse yesterday.

Bishop Murray is one of a number of auxiliary bishops criticised in the Murphy commission report into the handling of allegations of child sexual abuse in the Dublin archdiocese from 1975 to 2004.

Naughton, who featured strongly in the Murphy report, was yesterday sentenced to three years in prison, with one year suspended, for abusing a boy at least 70 times in Valleymount, Co Wicklow, between 1982 and 1984.

Parents who complained to Bishop Murray about the priest when he was an auxiliary bishop in Dublin in 1983 said they were dismissed by him.

Mervyn Rundle, who was abused by Naughton when the priest was moved from Valleymount to Donnycarney parish in 1984, yesterday asked “when are the guards going to act against these guys ?”

In 1998, Naughton was sentenced to three years in jail for abusing Mervyn Rundle and other boys in Donnycarney. The sentence was reduced by six months, on appeal.

Retired Garda sergeant John Brennan, who sought to have Naughton removed from Valleymount in 1984 following complaints by parents, said “as justice was done today, I think that it should now be taken a step further. Fr Naughton, I’ve always maintained, is a human being with a problem.”

He continued: “It was his superiors who, aware of this weakness, sent him around to other places, and I think they shouldn’t be allowed at this stage to resign or retire. They should be the subject of a criminal investigation. If there is neglect and evidence of a cover-up, it shouldn’t be a question of somebody resigning. They should be the subject of a criminal charge.”

A 78-year-old St Patrick’s Missionary Society priest, Naughton had pleaded guilty to five sample counts of indecent assault and yesterday received five three-year sentences, to run concurrently, with the final year suspended in each case.

Handing down the sentences at Wicklow Circuit Court in Bray, Judge Michael O’Shea said the abuse was “appalling, shocking and horrifying”.

The court heard that it started in 1982, when the victim was six years old. After he had made his First Communion he became an altar server in Valleymount parish, where Naughton was curate.

Judge O’Shea added that the abuse had an “absolutely catastrophic” impact on the victim’s life.

Last night, Archbishop of Dublin Diarmuid Martin said: “Tom Naughton was an abuser who damaged the lives of many innocent young people. I hope those involved in today’s proceedings will find some solace and justice in his having to serve a jail sentence for his crimes.”

Andrew Madden, who was abused by Fr Ivan Payne, said Donal Murray was Bishop in the archdiocese of Dublin during a time when the Murphy commission found that the sexual abuse of children by priests was covered up by the diocese and other church authorities.

"The structures and rules of the Catholic Church were found to have facilitated that cover-up," he said. The report tells us that some auxiliary bishops were made aware of complaints of child sexual abuse by priests in their geographical areas.

"It goes on to say other bishops found out about such priests through the regular monthly meetings involving the archbishop and the auxiliary bishops.

It is not believable to me that bishops attending those meetings were unaware that child sexual abuse was covered up by the archdiocese.

"They were bishops working in a diocese where children were sexually abused by priests that the diocese knew to be dangerous.

They were bishops that were part of a structure and culture that facilitated the sexual abuse of children.

They joined with other Bishops to issue a statement on 10th December 2009 to say they are shamed by the extent to which child sexual abuse was covered up in the Archdiocese of Dublin, yet individually they claim to have done nothing wrong.

"Their continued presence in office is an insult to every child sexually abused by a priest in the Dublin archdiocese, they display a contemptible level of arrogance and an inappropriate lack of humility.

"The Catholic church in Ireland has totally failed to respond at all appropriately to the findings of the Murphy report."

Mayor of Limerick Kevin Kiely said he wished to acknowledge "the contribution that Dr Donal Murray has made to the Diocese of Limerick over the last 13 years".

"Since he became Bishop of Limerick in 1996, Dr Murray has served the people of Limerick to the best of his ability and I would like to pay tribute to him for his hard work and dedication on behalf of the diocese.

"I am saddened by the circumstances which have led to Dr Murray’s resignation today after several days of reflection and I wish him well for the future."