But he failed to do so and instead he asked Roman Catholics around the world to be "indulgent towards sinners and pray to God to ask for forgiveness for our failings."
He used as an example the Bible parable from John's Gospel in which Christ asks people about to stone an adulteress: "Let he who is without sin cast the first stone."
However Corriere Della Sera's Vatican commentator Luigi Accattoli noted in an editorial how the Pope in his letter had "not asked for forgiveness as his predecessor sometimes did because he felt he was not responsible."
Mr Accattoli said Pope Benedict had used words such as "deeply disturbed" and "shocked and hurt" and picked up on the phrase where Pope Benedict wrote: "In the name of the Church I express my shame and embarrassment."
The pontiff didn't mention his letter chastising Ireland's church hierarchy as he made his weekly appearance Sunday from his studio window overlooking St. Peter's Square. He cited the Gospel passage about Jesus' inviting those without sin to cast the first stone toward an adulterer.
"While acknowledging her sin, he does not condemn her, but urges her to sin no more," Pope Benedict said. told English-speaking pilgrims in the square. "Trusting in his great mercy toward us, we humbly beg his forgiveness for our own failings, and we ask for the strength to grow in his holiness."
There has be a negative reaction to the letter in Ireland, which did not acknowlege a Vatican role in covering up sexual scandals.
Father Kevin Hegarty, parish priest in Co Mayo, spoke out against the Vatican's failure to address its mistakes.
"Overall the response would be 'thankfully he's said something at last'. People I've spoken to are appalled and ashamed by the cover-ups and people are just waiting to see what will happen after the Papal letter. Trust won't be rebuilt just by a Papal letter," he said. "I didn't have any great hopes of the letter, I thought the expectations about it were too high. I thought it was lucid and accessible and I thought his words to the victims showed real concern, however I think that only the victims can judge if it eased their pain in any way.
Cardinal Sean Brady, the head of the church in Ireland, is under pressure to resign. More revelations of wrongdoing as also stunned this week by disclosures that two other accused Irish priests agreed to pay thousands of pounds in out-of-court settlements to their alleged victims.
A German magazine quoted the head of the German Bishops Conference on Sunday as acknowledging that Roman Catholic church consciously covered up cases of sexual abuse.
Archbishop Robert Zollitsch of Freiburg said that while most cases happened outside the church, "assaults that took place in such numbers within our institutions shame and frighten me."
But a counterpart of Archbishop Zollitsch, Bishop Gerhard Mueller of Regensburg, instead accused the media of carrying out a campaign against the Catholic Church which was "comparable to that done by the Nazis."
His comments were surprising as his diocese includes the Regensburg Cathedral Choir which has been at the centre of German abuse claims.
It is also the same choir where the Pope's brother. retired priest Georg Ratzinger, was in charge for 30 years and he too has been tainted by the scandal admitting to "hitting some of the boys."
In comments published on the diocese website Bishop Mueller added:"Today from many parts of the media we see an attack on the credibility of the Catholic Church.
"This is carried out by the use of adapted facts and constant repetition of past events which would seem to imply that the Church is a nest of of corrupt people."
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