The abuse happened at institutions run by religious orders
The representatives of 18 religious orders named in the Ryan report into abuse have said they will pay victims further substantial compensation.
The orders met the Irish Prime Minister, Brian Cowen, on Thursday.
They had been told they would have to increase their contribution to a compensation fund of over 1.3bn euros.
The Ryan report revealed a catalogue of abuse stretching back decades at institutions the Roman Catholic orders had run on behalf of the Irish state.
Education Minister Batt O'Keeffe said all religious orders had apologised and agreed to co-operate fully with the government.
Mr O'Keeffe said the orders had agreed a mechanism to increase their contribution, and the process would be open and transparent. All congregations would have an independent audit carried out to examine their resources, he added.
Later, the orders said in a joint statement that they would "make financial and other contributions toward a broad range of measures designed to alleviate the hurt caused to people who were abused in their care".
"Each congregation is fully committed to identifying its resources, both financial and other, within a transparent process with a view to delivering upon commitments made today," the statement said.
They will hold talks with the Irish government again in two weeks.
There had been widespread criticism of a 2002 deal between the government, which capped the orders' contributions at 127m euros.
Mr Cowen told the orders he had to "express the dismay and abhorrence which, with the whole of the population, we have experienced on reading the report and the catalogue of suffering, deprivation and abuse which was the lot of so many children committed to institutions under the care of religious communities".
He said the "systematic nature of the findings, the sheer scale of the suffering endured by children and the grievous abuse of many of them" while in the care of religious orders meant that the bodies had a "moral responsibility to be faced".
On Wednesday night, Mr Cowen met groups representing victims of child abuse in the institutions.
He said that the congregations involved would make "substantial" additional contributions but did not specify a sum.
Another major report is due soon on abuse by Catholic priests working in parish churches around Dublin.
The Archbishop of Dublin, the Most Reverend Diarmuid Martin, warned earlier this year that it would "shock us all."