An opposition TD has said he may be one of the people affected by the "bombshell" revelations of illegal adoptions in Ireland.
Richard Boyd Barrett said he was "particularly struck by this scandal" as he was adopted via the agency involved.
The Irish Government announced on Tuesday that 126 people who had been adopted through the former St Patrick's Guild adoption society between 1946 and 1969, had incorrect details registered on their birth certificates.
The names of the people they were placed with were incorrectly recorded as their birth parents.
"I was adopted via St Patrick's Guild in the years affected," Mr Boyd Barrett told the Dail.
"I don't actually know if I'm one of the cases involved, probably not, but I have questions now, as do other members of my family, both adoptive and birth families."
"Thousands more have very serious questions to ask or are living in ignorance of their true heritage and are going to have events visited on them that are life-changing."
The Solidarity-People Before Profit TD said the people affected have had their identities stolen and their welfare comprised by not being told of their biological heritage.
Sinn Fein leader Mary Lou McDonald said once again Irish citizens were being faced with a "scandalous mistreatment" by the State.
"Many will want to know who their birth parents are and now it might be too late," Ms McDonald said.
She said the Taoiseach must ensure a comprehensive and properly resourced investigation into illegal adoptions scandal was carried out.
"A simple sampling exercise will not cut it," Ms McDonald said.
"These 126 cases account for only one organisation involved in adoptions in this state. There was an estimated 182 such organisations.
"This is potentially only the tip of the iceberg."
Mr Varadkar said an initial scoping and sampling exercise, looking at records of other adoption societies, would be carried out.
He said if there was any evidence, a full analysis of hundreds of thousands of documents, would take place.
"It's potentially a mammoth task," the Taoiseach said.
Fianna Fail leader Micheal Martin and the Labour Party's Jan O'Sullivan criticised the Government for the delays in bringing legislation through parliament to improve the rights of adoptees.
But Mr Varadkar said the 2016 bill had not stalled and that Children's Minister Katherine Zappone was treating it as a priority.
He said the minister would be briefing the Opposition spokespeople in relation to the issue in coming days in an attempt to speed up passage of the legislation.