In a statement, Abbot Kevin Smith, 64, of the Norbertine Community's Holy Trinity Abbey in Co Cavan, confirmed he had quit after 24 years in the post.
He acknowledged 'errors and failures' in dealing with the affair.
He expressed his 'deep sorrow and concern' for the victims of Father Brendan Smyth, a Norbertine priest for 40 years who was jailed in June for four years for sexual assaults on eight children from west Belfast over a 24-year period.
Despite knowing of the priest's paedophile activities, the abbot responded by re-assigning him to new posts without warning potential employers in job references of the danger he posed.
As a result there were further complaints of assaults against boys and girls after Smyth was sent to Rhode Island and Dakota in the United States from 1979 to 1983.
Cardinal Cahal Daly, the Irish Catholic Primate, has confirmed he received complaints about Smyth as far back as 1989. He has claimed that church structure meant only the Norbertine abbot was empowered to deal with Smyth.
The case has sparked a national outcry in Ireland, focusing attention on other alleged child abuse scandals involving clergymen. A government report is expected soon into alleged assaults at Madonna House, a Dublin children's home run by a religious order.
The Smyth case has also involved Harry Whelehan, the Irish attorney-general, whose 1992 decision to seek an injunction barring a pregnant 14- year-old rape victim from going to Britain for an abortion sparked an outcry.
Irish newspapers alleged that Mr Whelehan took no action on a file seeking Smyth's extradition from the Irish Republic to face charges in Northern Ireland. It was allegedly sent to him in May last year and involved offences going back 30 years, according to the Sunday Press newspaper.
Official legal sources were quoted as saying the proceedings had been shelved because 'we were told that he was going back to the North of his own free will. Then we heard he had disappeared'.