DUBLIN — Pope Benedict XVI’s weekend apology to sufferers of sexual abuse at the hands of the Roman Catholic Church in Ireland met with a deeply skeptical and often angry response from many Catholics here on Sunday, with one prominent victim calling it ineffectual and demanding that the pope forcibly remove the head of the Irish church if he does not resign.

In the apology, Benedict expressed “shame and remorse” to victims and their families for “sinful and criminal” acts committed by members of the clergy. His apology, a pastoral letter, was read aloud at all weekend Masses in the 26 Catholic dioceses spread across the Irish Republic and the six British-governed counties of the north, and handed out in printed form to thousands of churchgoers.

But in the apology, issued on Saturday, the pope did not require that Cardinal Sean Brady, who is the head of the Irish church, or any other church leaders be disciplined for their mistakes, as some victims had hoped. Nor did he clarify what critics in Ireland and elsewhere have said are contradictory Vatican rules about the procedures for investigating abuse cases within the church and church leaders’ responsibility to inform civil authorities about offenses they uncover, a duty the pope reiterated strongly in his letter.

By remaining silent on the issue of punishment for top church figures implicated in what critics in Ireland have described as decades of cover-up, the pastoral letter appeared to have done little to assuage the dismay and anger of many in Ireland at years of revelations about pedophiles among priests and those who care for children. While Benedict called for forgiveness, a common response among worshipers and nonworshipers alike was that there would be no healing until at least some prominent church leaders resigned.