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.