The Pope summoned the bishops for two days of meetings
Pope Benedict XVI has upbraided Irish Roman Catholic bishops over their handling of child sex abuse scandals.
He condemned abuse of children by priests as a "heinous crime", and said Irish bishops must act to restore the Church's "moral credibility".
During two days of meetings at the Vatican, the Pope reprimanded the bishops for a "failure... for years to act effectively", a statement said.
Last year the Irish Church admitted covering up abuse for decades.
Two state-ordered reports revealed how abuse was rife in many Irish Catholic-run children's institutions, and how priests who were accused of abuse were just moved by bishops to new parishes.
Investigators found that Church officials compiled confidential files on more than 100 parish priests accused of sexual abuse, but that the files were kept secret.
Victims of abuse have accused the Church of putting its own reputation ahead of concern for abused children.
'Honesty and courage'
Following three meetings with the bishops over two days, the Vatican released a statement saying: "All those present recognised that this grave crisis has led to a breakdown in trust in the Church's leadership."
By David Willey BBC Vatican correspondent
The proceedings were conducted in total secrecy, but we know from the official Vatican communique issued at the end of this extraordinary crisis meeting that the Pope strongly condemned the child abuse scandal.
The bishops promised the Pope that they were committed to co-operating with the civil authorities over the paedophilia scandal.
Pope Benedict lambasted the bishops for failing to act effectively over cases of sexual abuse of young people.
He wants "structural change"' in the organisation of his Church in Ireland, which has an unusually high proportion of bishops in proportion to its population.
The Pope had faulted "the failure of the Irish Church authorities for years to act effectively over cases of sexual abuse against young people", the statement said.
"For his part, the Holy Father observed that the sexual abuse of children and young people is not only a heinous crime, but also a grave sin which offends God and wounds the dignity of the human person created in his image.
"While realising that the current painful situation will not be resolved quickly, he challenged the bishops to address the problems of the past with determination and resolve, and to face the present crisis with honesty and courage."
The Vatican also said that the Irish bishops promised to co-operate with civil authorities, "to guarantee that the Church's standards, policies and procedures represent best practice in this area".
Father Federico Lombardi makes a statement on behalf of the Pope
Victims of abuse by Irish priests have written a letter to the Pope calling for the resignation of bishops "who engaged in this culture of cover-up".
"The lives of thousands of Irish people have been devastated by sexual abuse by priests," the letter said.
Four bishops have already offered their resignations - though only one has been formally accepted.
A spokesman said the issue of resignation was not discussed at the Pope's meetings with the bishops.
Victims of paedophile priests said the Pope's words must be followed by action.
"We are entitled to expect that the Pope makes those who committed crimes or covered up crimes, including bishops, be made accountable," said Irish Survivors of Child Abuse founder John Kelly.
"The words coming out at the moment seem to be positive. Whether they will act upon them and whether they will go far enough is another matter. We need to see the words turned into action," he told the AFP news agency.
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