The Irish Thalidomide Association has rejected a letter from the Government and said that it did not amount to an apology for what happened its members.
The letter was an expression of general regret, blaming the regulatory standards of the time, the ITA said.
Any expression of sympathy is not an apology, it added.
The association described an additional package of healthcare supports announced last week by the Government as inadequate and not set up on a statutory footing, and that no fair compensation scheme has ever been set up.
Spokesperson Finola Cassidy said that the ITA would take up an invitation to meet the Taoiseach next week.
There are around 40 thalidomide survivors in Ireland.
Dr Austin O'Carroll, also an ITA spokesperson, said that the Government has gone in the "wrong direction" with the letter that "was done like an apology and interpreted as apology, yet wasn't".
This has "really significantly hurt and caused a huge amount of anger," he said.
He added that the health care package deal should have gone before the High Court, as it involved children, and must be complete and fair.
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'Failure' to recall controversial drug
Thalidomide first became available in the late 1950s as a drug for sleeping problems and morning sickness but later became linked to birth defects.
The group said that 60 years on from the biggest medical tragedy, it is seeking justice for both the recognised survivors and those it is aware of who have been damaged by thalidomide but have not yet been officially recognised by the State or the German manufacturers of the drug.
The ITA believes there was a failure to recall thalidomide here in 1961, along with inadequate regulations and a failure to put a healthcare package of supports in place in 1975.
The Taoiseach has said the apology letter sent to thalidomide survivors is an invitation to come to Government buildings next week, and was not ruling out the prospect of a formal State apology.
He said that he has "nothing but respect" for the survivors.
"I very much look forward to meeting with them, to talk with them in person. I think they very much deserve that."
The Taoiseach said that the purpose of the letter, which was signed by the three party leaders, was to raise awareness for the enhanced health and social care supports available today, but "it's not the final word on the matter."
"What I wanted to do was mark progress in an area where we've made some over a sustained period of time around health and social care supports, [I’m] very conscious that there are other issues that remain outstanding. I want to meet the thalidomide survivors and I want to see in engaging with them how we can best move forward on that," he said.
