In a statement to be sent out to churches across England and Wales this weekend, the bishops said the abuse of children at the hands of clergy was a "profound scandal" that had brought "deep shame" on the whole Church.
"We express our heartfelt apology and deep sorrow to those who have suffered abuse, those who have felt ignored, disbelieved or betrayed," they said.
"We ask their pardon, and the pardon of God for these terrible deeds done in our midst. There can be no excuses."
The statement calls on Catholics in England and Wales to make the four Fridays in May "special days of prayer" for healing and forgiveness.
"We pray for all who have suffered abuse, for those who mishandled these matters and added to the suffering of those affected," the bishops said.
"From this prayer we do not exclude those who have committed these sins of abuse. They have a journey of repentance and atonement to make."
Two reports last year found that the Catholic Church in Ireland had deliberately failed to report the abuse of children by priests in a bid to protect its own reputation. Similar scandals have rocked the Church in recent months in Canada, Germany and Malta.
Pope Benedict XVI apologised for the abuse in Ireland in a letter to Irish Catholics last month, before finding himself at the centre of a row over whether he had covered up child abuse cases in the US in the 1990s. The Vatican has denied any wrongdoing by the Pope.
The scandal led to the resignation of a several Irish Catholic bishops, most recently the Bishop of Kildare and Leighlin, James Moriarty. He offered to resign in December after conceding that he had failed to change "the prevailing culture" while serving as auxiliary bishop in Dublin from 1992 to 2002. The Pope announced that he had accepted the resignation today.