Children's Minister Katherine Zappone says the scandal was uncovered from 'index cards on top of files'
The Taoiseach has warned that the illegally registered adoptions at St Patrick's Guild may only be the "tip of the iceberg."
Yesterday it was revealed 126 people had their adoptive parents registered as their birth parents, and may not know they are adopted at all.
An independent investigation is to look into the matter.
Speaking in the Dáil, Leo Varadkar said there will be a sampling exercise of other adoption agencies amid fears thousands of people may be affected.
"If that indicates [...] that there is evidence of these illegal registrations in other adoption societies, then we will do an analysis of those records," he said.
"It is potentially a mammoth task - that is the case - and it potentially is the tip of the iceberg.
"But I think again we need to be [...] sensitive in our language and not assume all of these things.
"Let's act quickly, but let's always act on the basis of the facts."
Earlier, the Children's Minister Katherine Zappone said the scandal was uncovered by Tusla workers who found index cards on top of files.
On Tuesday, it emerged that dozens of people placed for adoption in St Patrick's Guild may not know they are adopted.
The child and family agency Tusla has identified 126 cases where births were incorrectly registered by the former agency between 1946 and 1969.
They are cases where the adoptive parents of the child were recorded as the birth parents, without an adoption order.
A freecall helpline number has been set up by Tusla for people concerned on 1800-805-665.
Minister Zappone said they have received 85 callers so far, with most of those calls lasting up to an hour.
The helpline is open from 10.00am to 4.00pm Monday to Friday.
Speaking to Lunchtime Live on Newstalk, Minister Zappone outlined how this discovery came about.
"The Tusla child and family agency over the last couple of months have been working on files, looking at files from the St Patrick's Guild Society - one of the largest adoption societies in the history of the country - and in the course of that work effectively they found some language on index cards that sat on top of the files that said 'Adopted from birth' for certain individuals.
"That led them to suspect that it may mean that that person could have been effectively placed with a couple and registered as if that person were their own.
"And then what happened next is they did a lot of additional research in relation to the files, crossed-checked it with adoption authority people, brought in also the Registrar's Office.
"And as a result of all of that work, last week confirmed to me that they had really hard evidence that 126 indivisibles who were born between the years of 1946 and 1969 were placed with families as if they were their own."
She also confirmed 79 people may not be aware they are adopted.
Minister Zappone said supports are being put in place to help these people.
"At the heart of our identity and who we are - even thinking about my own parents and family, that shapes so much of who I am and I can't imagine if that was turned upside down.
"So given that, we have... (been) working with Tusla who have really specialised expert teams who have been placed on the cases of each of these 126 individuals, there's been a social worker assigned to each case.
"What they're going to do now at this moment, they are going through the file one more time, looking for the contact information for the individual who was placed with a family - but also for the adopted parents as well as the birth mother.
"So all of those people have to be contacted, and that it has to be done in a very sensitive and supportive manner - and in a way that when they are able to make that contact they know they're going to have to spend a lot of time speaking with them, trying to share that information in a way that they can absorb it and take it in".
Minister Zappone added that adopted parents will be contacted in the first instance, who will then be asked if they have shared this information with their child.
If not, they will be given the opportunity to speak to them first.
The Adoption Rights Alliance (ARA) has said the 126 illegal adoptions discovered represent "a mere fraction" of the total number of such cases.
While the Taoiseach Leo Varadkar has said it is far too early to be thinking about a redress scheme or free DNA tests for those caught up in the scandal.