Thousands of children were abused in institutions run by religious orders
A group of survivors of child abuse in the Republic has called on 18 religious congregations to give the Garda the names of members who violated children.
SOCA Ireland has said it also wants any files on abusers handed over.
Earlier, Taoiseach Brian Cowen said any additional voluntary contribution to compensation for victims from the orders must be substantial.
Eleven of the 18 congregations named in the Ryan Report on Child Abuse have now accepted Mr Cowen's talks invitation.
The Ryan Report documented decades of abuse in institutions run by religious orders over six decades.
The Christian Brothers have announced they will review how much more compensation they can offer to victims.
The Oblate Order also said it would devote more resources to compensate children abused in its care.
The order ran the Daingean Reformatory in County Offaly.
On Tuesday, Taoiseach Brian Cowen said orders must make more payments "in view of the moral responsibility they continue to hold in these matters".
The Irish government has also said it will implement all 20 of the report's recommendations and will meet with all of the religious orders to discuss how they can make further payments.
The Sisters of Mercy have said that they intend to accept the taoiseach's invitation to meet them and to continue to co-operate in helping people who were in their care while children.
In a statement, the nuns made reference to calls to provide more money.
The Sisters of Our Lady of Charity also welcomed the proposed meetings.
"We recognise the vital need to find new ways of addressing the extreme hurt being felt by so many people and we will do our utmost to this end," a statement said.
The Daughters of Charity said it welcomed the opportunity to meet Mr Cowen and unreservedly apologised "to any person who was abused and hurt while in our care as children".
The Sisters of St Clare have also confirmed their intention to make additional resources available to former residents.
"We again apologise unreservedly for the wrongs done by members of our congregation" said Sr Patricia Rogers Abbess.
"Our apology can not change the continuing pain of children now grown to adulthood shadowed by the past, but the current members of the congregation grieve for every child who did not experience the compassion, empathy and support they were entitled to expect from us," she added.
The Good Shepherd Sisters said they were "determined to respond in the most effective and meaningful way" to those who were abused while in their care.
The Presentation Brothers, who ran St Joseph's Industrial School in Greenmount in County Cork, also said they will work with the government on the issue.
The Daingean Reformatory in County Offaly was run by the Oblate Order
The Sisters of St Louis have also responded to the Taoiseach's call that congregations would be pressed for further contributions.
The Christian Brothers said they would enter into a six-week consultation process. It is understood that they could hand over properties worth tens of millions of euros.
In a statement the order said it recognised its "moral obligation" to former residents.
"The Christian Brothers accept, with shame, the findings of the Commission to Inquire into Child Abuse.
"The congregation is deeply sorry for the hurt we have caused - not just for the mistakes of the past, but for the inadequacy of our responses over recent years," said the statement.
In 2002 the 18 congregations responsible for the institutional abuse of children in Ireland struck a deal with government which capped their contribution to a compensation pot to 128 million euros.
An assistant Garda commissioner has been appointed to examine the potential for future prosecutions.
"Those accountable for such crimes - no matter how long ago - must also face the full rigours of the law," said Mr Cowen.