The congregations criticised in the Ryan Report have said they are willing to make 'substantial additional financial contributions' as reparation for abuse of children in their care.
Minister for Education Batt O'Keeffe, who attended the meeting between representatives of the Government and the religious orders today, said a transparent mechanism would be put in place to establish the assets of the congregations.
He said the religious orders had agreed to a trust being put in place for the contributions.
Minister O'Keeffe said that the Government will again meet the congregations in two weeks time, when it is hoped an indication will be given about how much will be available for contribution.
The discussions follow a meeting that abuse survivors had with Brian Cowen at Government Buildings last night.
Most of the 18 congregations, who are members of CORI, indicated they were willing to meet with Mr Cowen since he issued an invitation following the report of the Ryan Commission.
The Taoiseach told the survivors that he will keep them informed on his meeting with the congregations.
Chief Whip Pat Carey said this morning that he did not think there was a major discrepancy between his view of State and religious equally sharing the financial cost of the scheme and the view of Minister for Education Batt O'Keeffe.
Last night, Minister O'Keeffe declined to put a figure on the proportion of compensation the religious orders should shoulder.
The organisation Survivors of Child Abuse Ireland has said that regardless of the outcome of audits of the 18 congregations' assets, they should match the contribution of taxpayers to helping survivors.