Leo Varadkar has said it is too soon to talk about free DNA testing or a redress scheme for those affected by an adoption scandal.
It follows revelations about illegal adoptions at St Patrick's Guild.
The agency registered 126 couples as the birth parents of children they were adopting, between 1946 and 1969.
It's thought around 80 of the adopted children have never been told the truth.
The issue was discovered when Tusla officials sorting through 13,500 records registered between 1946 and 1968 found index cards containing the words 'adopted from birth'.
Incorrect Registrations of Birth: New Evidence in St Patrick Guild Records https://t.co/5ffoGGzugW
— Katherine Zappone (@KZapponeTD) May 29, 2018
Today, the Taoiseach 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".
Campaigners for adopted people are calling for a full Garda investigation of all adoption agencies.
Children's Minister Katherine Zappone says it's hard to estimate the true extent of incorrect registrations of birth because the practice was concealed.
Katherine Zappone. Image: RollingNews.ie
Today, Minister Zappone said supports are being put in place to help those affected.
She said: "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."
An initial investigation is being carried out to see if a similar situation exists in the records of other former adoption agencies.
Meanwhile, Tusla is operating a Freephone helpline for anyone seeking information, available on 1800-805-665 between 10am and 4pm on weekdays.