Two more Bishops who served as auxiliaries in Dublin have said they do not feel they should resign following the Murphy Report.
Bishop Raymond Field and Bishop Jim Moriarty of Kildare and Leighlin said they do not believe there is reason for them to step down
Yesterday colleagues Bishop Eamonn Walsh and Bishop Martin Drennan of Galway said the report does not criticise them.
There are no indications from Donal Murray about whether he intends to offer his resignation as Bishop of Limerick.
Meanwhile in Maynooth, Archbishop Diarmuid Clifford of Cashel and Emly said the Bishops would continue to ask for forgiveness from the public and seek to assure parents that children are safe in any church organisation.
The Bishop of Derry, Dr Seamus Hegarty said he would welcome an inquiry into abuse allegations in the Donegal Diocese of Raphoe - where he formally served.
Pope Benedict is scheduled to be accompanied by the heads of five Vatican departments when he meets Ireland's two Catholic Primates tomorrow.
Cardinal Seán Brady arrived in Rome this morning in response to last week's Papal summons to discuss the impact on the Church here of the Murphy Report on clerical child abuse.
Archbishop Diarmuid Martin is expected this evening.
At the end of the first day of their winter meeting in Maynooth, the Catholic bishops last night issued a statement in which they expressed shock at the scale and depravity of abuse described in the Murphy Report.
The bishops said they are shamed by the extent to which child sexual abuse was covered up in the Archdiocese of Dublin.
The statement also says they recognise that this indicates a culture that was widespread in the church.
Yesterday's talks were completely devoted to the Murphy Report.
In the absence of Cardinal Brady and Archbishop Martin, the remaining 30 or so bishops will today discuss other matters on the agenda.
Their meeting is expected to end in the late afternoon, although no further statement is expected in advance of the meeting in Rome tomorrow.
Elsewhere, Northern Ireland's Health Minister Michael McGimpsey has welcomed comments by the Irish Catholic bishops on measures that might be taken to ensure that all allegations of clerical sexual abuse of children are properly handled in future in the wake of the Murphy report concerning the Archdiocese of Dublin.
The Irish Bishops Conference in Maynooth said they wished the National Board for Safeguarding Children to explore with the relevant government departments and statutory authorities, north and south, a mechanism to ensure that the Catholic Church's current policies for protecting children represented best practice and that all allegations of abuse were dealt with properly.
The Archbishop of Armagh Cardinal Brady and the other bishops said they apologised to all those who were abused by priests as children, to their families and to all people who felt rightly outraged and let down by the failure of moral leadership and accountability that emerged from the Murphy report.
Mr McGimspey has been asked by the Stormont Executive to represent it in relation to all the issues arising from the report and to explore how they would deal with the issue of clerical and institutional abuse within Northern Ireland.
The Minister said the final decision on what approach is adopted to address clerical and institutional abuse in Northern Ireland would rest with the Executive.
He said his officials were preparing a paper for the Executive setting out options for dealing with the issue of abuse within Northern Ireland.
The Assembly agreed last month following a debate on the Ryan report that an assessment of abuse needed to take place within Northern Ireland. One Belfast solicitor has estimated there could be over 1,000 victims of child abuse in church and state-run institutions in the North.
Michael McGimpsey said in the interests of safeguarding children now and in the future and in the interests of seeing that justice was done, he would oppose any arrangement which protected the anonymity of child abusers and failed to result in criminal prosecutions of such individuals. He believed this view was now shared across all parties within the Assembly.
He said his officials had had some preliminary discussions with representatives of the National Board for Safeguarding Children within the Catholic Church about their proposal.
He said the bishops' proposal had the potential to provide the public with independent reassurance about how children are now protected within the Catholic Church.
Health and Public Safety Department officials will discuss with representatives of the National Safeguarding Board the possible implications for cases of abuse.
Mr McGimpsey said the Executive had a responsibility to protect children and vulnerable adults from abuse.
He hoped thet could achieve a consensus in the Executive on an approach which would meet the needs of victims while at the same time ensuring children were protected now and in the future from those who might pose a risk to them.