Maeve Lewis (centre) is executive director of One in Four
Groups representing victims of clerical abuse have given a mixed reaction to the Pope's letter to Irish Catholics about the issue.
Maeve Lewis of One in Four said that despite some positives she was largely "despondent" about the letter.
She said it had not sufficiently addressed the "cover-up" of paedophile priests by the church's hierarchy.
However, Patrick Walsh of Irish Survivors of Abuse said the letter was "unprecedented" and "encouraging".
Pope Benedict XVI's letter accused Irish bishops of having made "serious mistakes".
However, One in Four has said that the Irish primate, Cardinal Sean Brady, should resign following his alleged role in the cover-up of an abuse case.
He was present at two meetings in 1975 when alleged victims of serial paedophile Fr Brendan Smyth were sworn to secrecy about what had happened.
Ms Lewis said that she welcomed the Pope's call for the church to co-operate with the secular authorities.
"But we are very despondent that the Pope does not address the key issue, which is the church policy, right to the very top of the Vatican, to cover up sex abuse scandals to protect paedophile priests at the expense of vulnerable children."
She said the group was "astounded" at the Pope's comments about how clerical sexual abuse could be seen in the context of the secularisation of Irish society.
"This shows a complete misunderstanding of the dynamics of sexual violence, and creates little hope that the Church will ever respond effectively to the problem."
However, Mr Walsh said that while there would be "mixed feelings" about the
he felt it was "encouraging".
He said: "There is an awful lot of call to prayer as you would expect of course from a man whose stock in trade is prayer.
"But I cut through all that stuff and what I see here is a very important historical document, unprecedented in the history of the Holy See, absolutely unprecedented."
He added that he believed the Pope's comments meant that those guilty of abuse should face criminal prosecution.
"Clearly it is a demand by the Pope that those who are guilty of crimes against the young submit themselves to the demands of justice. I take that to mean secular justice."
Clerical abuse survivor, Andrew Madden said the letter "failed to address this issue at all seriously".
In a statement, he said: "The context is of course inappropriate, as by its very definition a pastoral letter is addressed only to practising Catholics and so ignores many other people who may in some way have been affected by this issue."
He added that a pastoral letter was not the way to respond to reports carried out by the Irish state which detailed "the rape, abuse and sexual abuse of children by priests and religious in this country and its cover up by Church authorities".
He added: "As I had anticipated the letter also fails to address any of the issues raised by myself and others in our open letter to the Pope last month, in advance of the Irish Bishops' trip to Rome."
Cardinal Brady was speaking at Mass in Armagh
Cardinal Brady has said he hopes the Pope's letter will be a chance for "rebirth" in the church.
Speaking at mass in Armagh on Saturday morning, he urged people to read it with "an open heart and in a spirit of faith".
He added: "No one imagines that the present painful situation will be resolved quickly.
"Yet with perseverance, prayer and working together in unity, the Holy Father says we can be confident that the Church in Ireland will experience a season of rebirth and spiritual renewal."
The Archbishop of Dublin said the letter was a "further step" in the healing process.
Archbishop Diarmuid Martin added: "I welcome the Pope's expression of apology and his recognition of the suffering and betrayal experienced by survivors.
"The Pope recognises the failures of Church authorities in how they dealt with sinful and criminal acts."