The Vatican has refused to accept the resignations of two Irish bishops who offered to quit over the Catholic Church's child sex-abuse scandal.

Auxiliary bishops Eamonn Walsh and Raymond Field announced their resignations on Christmas Eve, saying they hoped the gesture would help bring peace to the victims of sexual abuse.

The offer followed a report that archbishops had turned a blind eye to cases of abuse.

One priest admitted to sexually abusing over 100 children, while another acknowledged that he had abused on a fortnightly basis over 25 years.

Auxiliary bishops Walsh and Field initially denied their alleged role in hushing up one case of abuse, but then offered to quit after failing to receive support from the Archbishop of Dublin.

The Vatican has declined the offer, so they will remain in their jobs, but with revised responsibilities.

"This means that they will be available to administer confirmation in any part of the diocese in the coming year," Archbishop of Dublin Diarmuid Martin said on Wednesday (local time) in a letter to priests in his archdiocese.

Martin Long from the Catholic Communications Office confirmed the contents of Archbishop Martin's letter, but said he could give no further information on what the bishops' "revised responsibilities" would be.

In March, the Pope issued a pastoral letter condemning child sex offenders within the Church, but he refused to acknowledge any culpability on the Vatican's part.

- ABC/AFP