In an open letter to a Belfast newspaper, Fr. Patrick McCafferty said Connell, who is also archbishop of Dublin, and other senior bishops should go because they are “not fit to lead the people of God.”
McCafferty suggested that they should follow the lead of Cardinal Bernard Law, the archbishop of Boston, who resigned last week.
He said no matter who was involved, including Connell in Dublin or Britain’s Cardinal Cormac Murphy-O’Connor in Westminster, he should look to his position in reparation to God for what should have been done.
“They will one day be accountable to God,” McCafferty later told the BBC. “I am only concerned about the children, because those children who have been abused, who have been raped, are still alive. Even though they are adults, they living with indescribable suffering.
“These men, like Bernard Law, whoever they are, wherever they are, get out. Because you are not fit for office. Take his example and get out.”
McCafferty said church leaders have not sufficiently acknowledged the intense suffering caused to victims of abuse.
“They have protected their own positions,” he said. “I am just an ordinary priest in a parish. I’m a little nobody as far as they are concerned, but I am sick of the whole thing and the people of God are speaking out.
“What in the name of almighty God did they think they were doing in moving these men about from place to place who were leaving a trail of misery and damage in their wake?”
However, abuse victim groups are split on the issue of resignations. The Irish Survivors of Child Abuse also called for resignations, saying it is clear that both Connell and Murphy-O’Connor have lost the confidence of their flock.
It said that if Connell does go, it must not allow him to “escape accountability or justice for his involvement in the crimes against children or to simply repeat his meaningless forgiveness to victims aligned to his legal apologies.”
Spokesman John Kelly said the circumstances of Law’s resignation are not dissimilar to the situation that Murphy-O’Connor and Connell found themselves in.
“Furthermore it is equally clear, both Cardinals failed to protect children from known religious pedophiles,” he said.
Kelly added that while Law’s decision to go was correct, his resignation came about only after victims had to “drag him screaming to be made accountable.”
But Colm O’Gorman, director of the victims group One in Four, said resignations now would solve nothing. What is needed, he said, is for the Vatican and the wider church to be accountable for what happened.
“What we are dealing with here is institutional corruption,” O’Gorman said. “We are dealing with an institutional failure and not a failure of individual clerics.
“Individual resignations at this point, before the issue has been dealt with appropriately and properly, are really just a distraction. They don’t resolve anything.
“What we need to see, rather than retribution and heads on platters, is atonement. We need to see the church come out, hold its hands up and acknowledge all of this.”
O’Gorman said it would then be a matter for the church to look to its own house and perhaps discuss resignations.
Fr. Martin Cosgrove, chairman Dublin Diocese Council of Priests, said in a statement he “emphatically” rejected calls for the resignation of Connell,
“Whilst he himself has been the first to acknowledge the mistakes made in the past and the suffering of all those concerned, we recognize how proactive he has been in addressing this grave and complex problem,” Cosgrove said. “For example, he established the Independent Diocesan Advisory Panel in 1996 to deal with every case of child sexual abuse by priests of this diocese.
“As Mr. David Kennedy, chairperson of the Panel, said: ‘All substantive recommendations made since then by this independent panel . . . have been accepted in full by Cardinal Connell.’
“Cardinal Connell’s integrity is widely recognized throughout the diocese and beyond. Two inquiries have been proposed to examine how the Dublin Archdiocese has addressed the issue.
“We feel that these should be allowed to take their course and establish the truth.”
Law is the most senior Catholic Church figure to resign since Vienna’s Cardinal Hans Hermann Groer went in 1995 after accusations that he once sexually molested a boy.
Clerical sex scandals or the handling of them has so far led to the resignations of 19 bishops worldwide.
The only Irish bishop to have resigned is Brendan Commiskey, formerly of Ferns. He stepped down last Easter after controversy about how he dealt with pedophile priests in his diocese.