Cardinal Sean Brady said he was following bishops' orders
The head of the Catholic Church in Ireland is facing further pressure to resign after he admitted knowing about the sexual abuse of two children.
Cardinal Sean Brady has said he was at meetings in 1975 where two abused children signed vows of silence over complaints against Fr Brendan Smyth.
The Rape Crisis Network Ireland (RCNI) said his position had become untenable.
TUV leader Jim Allister and Sinn Fein MLA Sue Ramsey have also said Cardinal Brady should consider stepping down.
The Irish Labour party said the police should investigate Cardinal Brady's role in the internal church inquiry into Fr Smyth.
The party's spokeswoman on social and family affairs, Roisin Shortall, said the cardinal was "hopelessly compromised by what had emerged".
"I believe that there should be a Garda (Irish police) investigation to determine whether or not the failure to report Fr Smyth's crimes to the civil authorities was, itself, a criminal offence," she said.
"I am advised that the administering of an oath requiring these children not to disclose the abuse to anyone else may also have constituted an offence."
Meanwhile, an Irish telephone helpline has recorded a significant increase in calls following the latest revelations about how the Catholic Church dealt with paedophile priest Brendan Smyth.
The Rape Crisis Centre in Dublin said it had to bring in extra staff to cope with the rise in calls on Monday night.
Cardinal Brady was involved in investigating complaints of abuse in his capacity as secretary to the bishop of Kilmore.
The two children at the centre of the case are reported to have been aged 10 and 14 when the investigation took place in 1975.
Cardinal Brady said he believed the victims and in his limited role did all he could to make sure Fr Smyth was stopped from working as a priest.
He said it was not fair to judge him by the child protection standards of today.
He added that as a relatively junior cleric it was not his responsibility to report Smyth to the police and that he passed all relevant information to his superiors.
Smyth's child abusing continued for many years after 1975.
The cardinal's critics have rejected his explanations.
"Cardinal Brady is personally implicated in collusion with clerical child sexual abuse," RCNI director Fiona Neary said.
"In recent public statements regarding clerical child abuse he did not make public his role in pressuring and bullying victims to remain silent. He did not make public his own failures to disclosure a known abuser to civil authorities.
Pope Benedict has had to deal with sex abuse scandals in various countries
"Sexual abuse that could have been prevented was not, and Brendan Smyth continued to abuse children."
Not a resigning matter'
Writer and broadcaster Father Brian D'Arcy, who is a rector of the Passionist Monastery at the Graan in Enniskillen, said he believed Cardinal Brady was in a difficult position.
"I have this awful picture of two young children who had already been abused by a cleric in a Roman collar now having to tell that abuse to two or three different clerics taking notes and then being asked to solemnly swear that it would be secret.
"Now if Canon (church) law demands that, then Canon law is wrong."
However, former Canon law professor, Monsignor Maurice Dooley, has also said Cardinal Brady was right not to have gone to Irish police with the allegations.
Monsignor Dooley said that as Fr Brady had been conducting in-camera investigation within the Church, he would have been violating his responsibilities if he had reported what he knew to the police.
Monsignor Dooley also said other, more senior people, people were responsible for the subsequent crimes of Fr Smyth.
The revelations come as the Catholic Church worldwide grapples with accusations that it covered up abuse by priests.
In recent months paedophile scandals have rocked the church in Ireland, the Netherlands, Austria and Germany.