Children's Minister Barry Andrews has said the Pope's pastoral letter did not go far enough to acknowledge weaknesses within the Church.
It is the first response from the Government on the pastoral letter issued on Saturday to address the matter of clerical child sex abuse in Ireland.
While he welcomed the tone of the letter, and the apology, Minister Andrews said that some areas were not covered.
"It (the letter) was obviously quite detailed, and yet there was an awful lot that wasn't detailed," Minister Andrews said.
"Issues to do with institutional weaknesses in the Church, I think, were not addressed, and naturally there were some people that were dissatisfied with it.
"But on the positive side, it was a very fulsome apology and I think, probably a genuine apology."
Minister Andrews also questioned the role of celibacy in the sexual abuse of children by priests and the religious.
"I think everybody is of the view that the issue of celibacy creates pressures on the human condition that are very hard to cope with, and I would like to have seen it addressed in some way," he said.
But Director of One in Four Maeve Lewis has rejected that.
"I actually think that the issue of celibacy is overplayed in this regard," Ms Lewis said.
"There are many people who are celibate in all walks of life. That doesn't necessarily mean that they are going to sexually abuse children."
Meanwhile a survivor of clerical abuse said today he believes the Pope is not fully aware of the abuse problem in Ireland.
Michael O'Brien, a spokesman for the Right to Peace Organisation, said he believes the Pope took the wrong approach.
"If he knew… that letter would have been a completely different letter," Mr O'Brien said.