The Coalition of Mother and Baby Home Survivors is calling on the Government to take urgent action to address the issue of illegal adoptions.
CMABS spokesperson Paul Redmond said no progress has been made in the past four years.
Speaking at a press conference in Dublin, Mr Redmond called for implementation of the Adoption Information and Tracing Bill.
The legislation would allow adoptees secure information about their adoptions.
The Government has denied stalling the legislation.
Minister for Children Katherine Zappone has told the Dáil the bill should pass through the Oireachtas by the end of the year, if there is co-operation across the Dáil and Seanad.
Mr Redmond also wants all records, even in privately owned institutions, to be secured along with a full national DNA database.
Independent Socialist TD Clare Daly told the press conference that illegal adoptions have been an open secret for years, saying "it's abundantly clear illegal adoptions were widespread".
She said revelations today of more concerns about hundreds of adoption cases is just the "tip of the iceberg".
The Irish Examiner is reporting that Tusla has raised concerns about 748 cases from St Patrick's Guild.
Last week, it emerged that between 1946 and 1969 some people placed by the former adoption society St Patrick's Guild had incorrect information registered on their birth certificates.
A spokesperson for Minister Zappone said that intensive efforts are under way this week to get the adoption information legislation through the Oireachtas by the end of the year.
The spokesperson said that Ms Zappone met advocacy groups yesterday, will meet politicians tomorrow, and the issue will be raised in the Dáil this week.