The Government Chief Whip has said that they will now attempt to return the compensation scheme for abuse victims to the 50-50 approach originally proposed by the Department of Finance.
Pat Carey told tonight's RTÉ The Week in Politics Programme that he hopes this approach will get the backing of all the political parties.
This could mean the Government would secure substantial additional contributions from the 18 religious orders who were party to the agreement signed in 2002.
To date it has seen them agreeing to contribute €128m out of a total cost of around €1.3bn.
Mr Carey said that over a period of time schools which are run by either trusts or religious orders should ultimately become part of a State system.
One of the leaders of the Christian Brothers in Ireland earlier called for more resources to be made available to provide compensation to victims of abuse.
Br Edmund Garvey made the comments in an interview on BBC Radio Ulster.
An agreement was reached between the religious orders and the Government in 2002 which limited the amount of money they would have to pay victims of abuse.
Under the deal, the contribution of the religious orders to the Redress Scheme was capped at €127m. It is estimated that the State will end up paying around ten times that amount.
In an interview with the Sunday Sequence programme, Br Garvey also said criminal prosecutions should be brought against those guilty of abusing children.
The Ryan Report, which runs to almost 3,000 pages, detailed how thousands of children in residential institutions run by religious congregations lived in a climate of fear.
The inquiry found that sexual abuse was endemic in boys' institutions and a chronic problem in some other residential institutions.
More educational support
A leading nun has said the 18 congregations are willing to provide more educational support for survivors and their families.
Sr Elizabeth Maxwell said that if the congregations had known in 2002 what they know now about how children in their care had been abused, the agreement it struck with Government would have been different.
The Presentation Sister, who led negotiations on the 2002 deal capping the contributions to the State's compensation fund, said the deal was not a mistake but added that it may be inadequate in light of what the report revealed 11 days ago.
The Congregations are to meet the Taoiseach on Thursday, a day after he consults survivors' groups.