The Sisters of Mercy are to contribute property and cash to the value of €128m by way of reparation for the suffering of children while they were cared for by the congregation in Industrial Schools.
The nuns say they are deeply saddened by the findings of last May's Ryan Report and reiterate their wholehearted apology for the suffering experienced by the children in their care.
This offer is the largest so far by any of the 18 Catholic religious bodies whose institutions were severely criticised for systemically abusing children in their care.
It follows a demand by the Taoiseach Brian Cowen for substantial contributions to the welfare of survivors and their families on top of their donation of €33 million to the state's €1 billion-plus Redress Scheme.
The Mercy Sisters ran five of the schools indicted, including Goldenbridge, one of the largest and most notorious in the country.
The Congregation has said that it will immediately engage with the voluntary groups to whom it has decided to transfer properties while it awaits confirmation from the Government regarding the transfer of assets to the State and to the independent trust.
Meanwhile, The Brothers of Charity have offered to contribute an additional €1.5m in cash to help victims of abuse in Catholic-run residential institutions.
The Ryan Report found that the congregation had covered up for paedophile brothers who abused children with special needs in residential care in Lota in Cork and Renmore in Galway.
In a statement on their website, the Brothers say their contribution represents three-quarters of their total net assets.
Dáil debating report
Meanwhile, The Dáil has been debating the findings of the report of the Commission of Investigation into the Catholic Archdiocese of Dublin.
In her contribution to the debate, Fianna Fáil TD Mary O'Rourke was strongly critical of the Catholic Church.
Deputy O'Rourke said the Church had lost affinity with its people with what she described as 'out-of-date and conformist rules', particularly on remarriage for divorcees and contraception.
She said until the Church reasserts itself as relevant in people's lives, it is doomed to failure.
Green Party TD Ciarán Cuffe has said he believes it is inappropriate for the Archbishop of Dublin to chair the National Maternity Hospital in Holles Street in Dublin.
Deputy Cuffe said he believed it was time to look carefully at putting in place alternative mechanisms.
He said responsibility for the 'crime of an appalling scale' uncovered in the report must go to the top of the Church.
Fine Gael's Alan Shatter accused the Taoiseach of showing undue deference to Church authorities and the Vatican.
Speaking on RTÉ's News at One, Mr Shatter said Brian Cowen should have been critical of the Vatican's insistence on using diplomatic channels in relation to inquiries on abuse issues.
Mr Shatter also said it was essential that the Papal Nuncio should appear before an Oireachtas Committee to help the future work by the Commission into clerical child abuse.
Murray insists his conscience is clear
Bishop of Limerick Donal Murray has said he has a clear conscience about his role in relation to the activities of a number of abusing priests in the Dublin Archdiocese when he was Auxiliary Bishop there.
However, he told the Limerick Leader newspaper that the one case that caused him 'constant anguish' was that of Fr Thomas Naughton.
He said he had apologised to people in Donnycarney, Ringsend and Valleymount in 2002, and said that he was unable to do more about the activities of this priest.
Bishop Murray said he was now in a 'listening process' and would gauge the opinion of the Diocese of Limerick and public opinion nationwide.
He added that he wanted to hear in particular from the victims in Dublin.
He said he would listen to what people had to say but he still had to make his own decision about whether he could be Bishop in Limerick in the light of all this.
The family of a deceased abuse victim has made an emotional call for Bishop Murray to stand aside.
Peter McCloskey's family say the Murphy Commission should also investigate the Limerick diocese.
Peter McCloskey died by suicide in April 2006, after repeated attempts to seek redress for the sexual abuse he suffered at the hands of a priest in Caherdavin parish in Limerick.
Archbishop Diarmuid Martin's has challenged ten serving and retired bishops to explain whether they should resign in light of their handling of clerical child sexual abuse while they were prelates in Dublin.
The interview with Donal Murray was published in yesterday's Limerick Leader.