Archbishop of Dublin Dr Diarmuid Martin has said the meeting between Pope Benedict XVI and Irish bishops in the Vatican in recent days was part of a process.
Speaking after an Ash Wednesday Mass at UCD, Dr Martin said the meeting will be followed by a pastoral letter and other things will happen, but not everything could happen right away.
He said the letters received from survivors were presented to the Pope, and they will be looked at.
Dr Martin said there was no turning back or denial of the Murphy report, which was one of the requests made by survivors.
He said the question of the Pope meeting with survivors was not excluded, adding that the Pope has met with survivors in a number of countries and these meetings have been announced afterwards to avoid the fact that it could become a media event.
Asked why the Pope had not issued an apology to Irish victims, Dr Martin said the tone of the meeting clearly stressed that this was a moment of great concern.
He added that 'there comes a time when repeating the word apology may even be empty'.
Dr Martin said the Pope was distressed at what had happened here in Ireland, particularly in the diocese of Dublin, and at what was recorded in the Murphy Report.
He said the meeting had been called to begin a process of seeing where do we address the problems that were there, why did it happen and where are we going to go in the future?
Dr Martin said he would not agree that the meetings were a wasted opportunity.
He said if victims feel dismayed, they have a right to feel dismayed. But he said he will listen to their dismay.
Dr Martin added that the hierarchy has 'begun something', and expressed he hope that now that dialogue has begun with survivors groups, that they don't lose heart.
Asked about why there was no discussions about resignations at the meeting, Dr Martin said it was said in advance of the meeting that that wouldn't happen.
He said that was a matter between those who present their resignations and the Pope.
He said standing down and resigning is a personal decision, involves people assuming accountability and responsibility, otherwise it is not resignation.
Drennan will not resign - spokesman
A spokesman for the Bishop of Galway, Dr Martin Drennan, told RTÉ News tonight that he would not be resigning from his position.
Bishop Drennan has been under pressure from organisations representing victims of clerical child sexual abuse to tender his resignation to the Pope.
Bishop Drennan's spokesman said he had not tendered his resignation to the pope during his visit to the Vatican and his position on not regisning from office was as he had previously outlined.
Survivors of abuse near 'despair'
The Rape Crisis Network has said victims of clerical sex abuse are in a 'state of almost despair' today following the outcome of the meeting between Pope Benedict and the Irish bishops.
Read the Vatican statement
Executive Director Fiona Neary said victims she had been speaking to this morning were deeply disappointed that the Pope had not accepted the responsibility, which she said the Vatican had in relation to child sex abuse in Ireland.
Irish Survivors of Child Abuse welcomed that the Pope finally acknowledged that paedophilia within the church is a 'heinous crime'.
However, it accused the Pope of failing to show strong leadership in tackling this crisis.
Clerical abuse survivor Andrew Madden has called for an urgent meeting with Dublin Archbishop Diarmuid Martin to find out why issues raised by victims were not addressed by the Pope.
Abuse helpline numbers
The Pope is preparing a pastoral letter to the Catholics of Ireland, taking into account the comments of the Irish bishops, which will be issued before Easter.
After yesterday’s meeting with the Pope, the Primate of All Ireland Cardinal Sean Brady told a news conference that the abuse of children by priests and religious was not just an Irish problem or a problem of the English-speaking world.
He said the Pope emphasised the need for the Bishops to be united in the face of the abuse crisis.