Independent TD Clare Daly has tabled a Dáil motion calling on the Government to establish an inquiry into the falsification of documents regarding adoptions and forced adoptions.
Speaking in the Dáil, she said it has been five years since the Government promised to investigate the Mother and Baby homes but she said survivors feel nothing much has changed.
The Commission of Investigation was set up following revelations in 2014 about the deaths of almost 800 children at the Tuam mother-and-baby home in Co Galway.
Deputy Daly told the Dáil there needed to be scrutiny of illegal adoptions in particular beyond the scoping exercise that the minister has committed to.
She called for illegal adoptions to be included in the terms of reference for the Commission of Investigation.
Deputy Daly also called for a redress scheme to be rolled out for survivors.
She said the continued delays in the publication of the Commission of Investigation's findings is pushing back the possibility of a redress scheme on an aging population who she said cannot wait.
In response, Minister for Children Katherine Zappone said the issues of Mother and Baby homes have left a stain on our nation.
She said the Commission of Investigation has sufficient power and scope to examine and make determination on a broad range of concerns.
She said five interim reports have been prepared to date, all of which have been published.
Minister Zappone said the commission makes no definitive finding of abuse or neglect in these reports and the Government would await its final report, which is due to be published by February 2020.
She said the House should not prejudge the Commission's work and that Government will respond to its findings and recommendations.
Minister Zappone said the motion was well-intentioned but was not as straight forward as Deputy Daly suggested.
She said there had been calls for redress for the survivors and some do not see it as necessary that the commission completes its work before these issues are dealt with.
Fianna Fáil TD Fiona O'Loughlin said the Commission of Investigation into Mother and Baby homes must be allowed to finish its work before any action is taken which would undermine the work of its investigation.
She said the postponement of the Commission of Investigation's report was "deeply distressing" for elderly survivors.
However, she said it was in the best interest of survivors that the commission be given time to finish its work before making any recommendations regarding redress.
Sinn Féin TD Denise Mitchell said the treatment of women and children in Mother and Baby homes was "deeply shameful".
She said the fact that so many children were illegally adopted to the US, Britain and elsewhere was "shocking".
She said there was growing frustration at the failure of the Government to deal with redress.
Deputy Mitchell said this is compounded by the consistent delay of the commission’s final report and the insistence that redress will only be considered after the final report is published.
Labour’s Joan Burton said the scandal of the illegal birth registrations are of huge concern and she said people were "stupefied" by the lack emotional intelligence in how the Government is responding to the issue.
People Before Profit TD Richard Boyd Barrett said he could not see why the work of the Commission is preventing things being done now.
He said we should not have a situation where justice and redress is delayed to a point where it’s too late.
Independent for Change TD, Catherine Connolly, said she was "frustrated" with the Government’s response to deal with redress until after the Commission publishes its report.