The Bethany Home Survivors Group says the Taoiseach's decision to carry out a sampling exercise of other adoption agencies is a step in the right direction.
The group says those who've been affected by the adoption scandal at St Patrick's Guild should be part of a redress scheme.
126 people had their adoptive parents registered as their birth parents, and may not know they're adopted at all.
The group's chairperson Derek Leinster says he's pleased with Leo Varadkar's commitment.
"It's good that he's now recognising and it's a step in the right direction if he says he's going to looking into other adoption things.
"You know something: it needs to be looked into very severely".
Taoiseach Leo Varadkar at a press briefing for the launch of Ireland Project 2040 | Image: Sam Boal/RollingNews.ie
However the group have rejected Mr Varadkar's assertion that it is too early to consider redress or free DNA tests for those affected by the illegal adoption scandal.
Yesterday, Mr Varadkar said: "I think it's far too early to be talking about things like DNA tests or redress schemes.
"The sense that I have from people who have been affected by this is they're not looking for money from the taxpayer or they're not looking for retribution: they're looking for information about their identities.
"They want to know who they are, they want to know what their birth story is".
But the CMABS said: "Once again, the Government's instant response to survivors and victims is to fob them off and began the endless series of excuses, stalling, scoping exercises and sub committees, while illegally adopted people and their natural mothers continue to die by the hundreds.
"Illegally adopted people are the victims of crime and as such, have a right to 'legal remedy' under domestic and international law."