The Roman Catholic order of Christian Brothers, once the largest provider of residential care for boys in Ireland, said it offered a package of 161 million euros (146 million pounds) in compensation.
But the Irish Survivors of Child Abuse group (SOCA) said only 34 million euros of the offer was "new money."
Disclosures in May of floggings, slave labour and gang rape in much of Ireland's now defunct system of industrial and reform schools have shamed Irish people and put pressure on religious orders who ran the institutions to pay more for past abuses.
A string of scandals involving priests molesting young boys have eroded the Catholic Church's moral authority in Ireland, once one of the most devout countries in the world.
The Christian Brothers said it would pay 30 million euros into a government trust, 4 million for counselling and transfer school playing fields worth 127 million to a government trust.
"The range of incremental measures outlined above follow the Christian Brothers' acceptance, shame and sorrow at the findings of the Ryan Report," the order said in a statement, referring to the inquiry covering the period between the 1930s and 1970s chaired by High Court Justice Sean Ryan.
The order said the offer would bring its total contributions since 1996 to 191 million euros.
But SOCA said: "This morning's statement from the Christian Brothers is an exercise in the art of sophistry by its supreme practitioners in Ireland."
It added: "The references to playing fields to be held in joint trust with the State has nothing whatever to do with redressing the victims of Christian Brother abuse in Irish institutions."
Two other groups -- the Sisters of Charity and Daughters of Charity -- later said they had pledged to contribute 5 million euros and 10 million euros respectively for the benefit of former residents of religious-run institutions.
The moves came as Ireland awaits the publication of a separate report on the handling of allegations of child sex abuse in the archdiocese of Dublin from 1975 to 2004, which Prime Minister Brian Cowen said would be published on Thursday.
"In these days we will be reading of sordid events that took place within the Catholic Church in the Archdiocese of Dublin," Archbishop Diarmuid Martin said at a ceremony last week.
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