Children's Minister Katherine Zappone has urged people with information on burials at former Mother and Baby Homes to come forward.
Her plea comes after a commission of investigation found that the resting place of the "vast majority" of the hundreds of children who died at the Bessborough home in Cork is not known.
Responding to the commission's findings, Ms Zappone appealed to those with knowledge of the homes to "let us know where [the babies] are buried".
"Maybe then, finally, they could be treated with dignity in death," she said.
The commission's fifth interim report also found that many of the 800-plus children who died at the Tuam home in Co Galway are likely to be buried inside a decommissioned sewage tank.
Taoiseach Leo Varadkar described the report as "gruesome reading".
He said Irish society inherits a "deep shame" for what was done at the institutions at a time when women and babies were "appallingly treated", often for being unmarried or poor.
The report criticised religious orders that ran the institutions. It also criticised Galway County Council which owned the home at Tuam.
The Congregation of the Sacred Hearts of Jesus and Mary owned and ran three institutions: Bessborough; Castlepollard, Co Westmeath; and Sean Ross, Co Tipperary.
It provided the commission with an affidavit about burials generally and specifically about those at Castlepollard and Sean Ross.
The report said that the affidavit was "in many respects, speculative, inaccurate and misleading".
The commission said more than 900 children died in Bessborough - or in hospital after being transferred from the institution - over more than seven decades.
The report said the Congregation of the Sacred Hearts of Jesus and Mary do not know where the children are buried. The commission considers it likely that some of the children are buried in the grounds of Bessborough, but has been unable to find physical or documentary evidence of this.
The Sisters of the Sacred Hearts of Jesus and Mary issued a statement last night, insisting the commission "has had and will continue to have our fullest co-operation".
The commission's report said 802 children died at the Tuam institution.
Many of the children are said to have been buried in a chamber structure built within a large decommissioned sewage tank. It is not believed the tank was designed as a burial chamber.
The commission said it did not provide for the dignified interment of human remains.
The report said the Sisters of Bon Secours - which ran the Tuam home - were "unable to provide any information about the burials there".
The commission also said they are "surprised by the lack of knowledge about the burials on the part of Galway County Council" and the nuns.
"There must be people in Tuam who know more about the burial arrangements and who did not come forward with the information," it said.
It concluded there is little basis for the theory that rather than having died that children were 'sold' to America.
A statement from the Bons Secours Sisters said they have "always cooperated fully with the commission of investigation and will continue to do so.
"Every piece of information we have on the Tuam home we have shared with the commission."
Galway County Council did not respond to a request for comment.