Dr John McAreavey was Bishop of Dromore. Diocesan secretary Fr Gerald Powell said he had resigned with “immediate effect”.
Fr Malachy Finnegan has been accused of sexual abuse by 12 people.
The bishop said: “Following media reports which have disturbed and upset many people in the diocese and further afield, I have decided to resign with immediate effect.
“I shall make further comment in due course.”
The former teacher at St Colman’s College in Newry from 1967 to 1976 is also allegedly linked to a catalogue of physical and emotional abuse against pupils. He died in 2002.
Amnesty International has called for a public inquiry into clerical sex abuse.
Amnesty’s Northern Ireland director Patrick Corrigan said: “To date, clerical abuse victims here have been let down, not just by the church, but also by the authorities.”
Solicitor Claire McKeegan, of KRW Law, who represents a number of Fr Finnegan’s alleged victims, said she had received calls from numerous further witnesses since a settlement by one of her clients was made public recently.
She added: “The message is clear: victims demand a public inquiry into clerical abuse in Northern Ireland without any further delay.
“The victims and survivors deserve to speak about the horrific abuse that took place and be heard in a public forum tasked with sufficient powers to get to the truth.
“This case has brought to the surface yet another paedophile priest who was never investigated or exposed by the church or the police.”
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A Catholic bishop in Northern Ireland has resigned following claims he celebrated Mass alongside a priest he knew was a paedophile.
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