The Mother and Baby Homes Commission says it is legally prohibited from informing any surviving family members of the children they have found burial locations for.
It comes as the investigation's fifth interim report revealed that, of the 900 infants who died in Bessborough or in hospital after being transferred from Bessborough, the Commission can only find the final resting place of 64 babies.
Theasked the Commission if it can inform any of the surviving family members, where they exist, of the final resting place of their relatives.
In a statement, the Commission said that the Commissions of Investigation Act provides that it is "an offence for anyone, including a member of the commission, to disclose or publish any evidence given or the contents of any document produced" and that, as a result, "we cannot inform the families".
"In any event, in the vast majority of cases, we would have no information about the families; it perhaps should be noted that, apart from the mothers (the vast majority of whom are likely to be dead since the vast majority of deaths occurred before 1950), family members may never have been aware of the existence of the deceased child," reads the statement.
Five children from the Bessborough institution were buried in St Finbarr's cemetery in Cork city on dates between 1976 and 1990. These burials were revealed by the Irish Examiner in February of last year.
It emerged on Thursday that the sister of a baby boy who died in Bessborough only found out that he was buried in a former famine grave via the Commission's burials report.
Carmel Cantwell's brother, William, was just six weeks old in December 1960 when he died in St Finbarr's Hospital in Cork after having been born in the Bessborough Mother and Baby Home. In the mid-1990s, Carmel's mother went to the nuns requesting documentation about her time in Bessborough and seeking information as to where her son was buried. She was told he was buried in Bessborough in the small burial plot belonging to nuns.
However, it was revealed in the report that William is in fact buried in Cork District Cemetery, Carr’s Hill and that this was confirmed in a letter dated December 12, 1994.
Ms Cantwell is now seeking confirmation of the location of her brother's burial from the Commission.
The Irish Council for Civil Liberties has called on justice minister Charlie Flanagan to "mandate individual criminal investigations" and to ensure that where the law was broken or where human rights abuses have occurred, that accountability for this is ensured.
It is deeply regrettable that because of the strict rules on the use of evidence gathered by the Commission, witnesses in such cases would need to be re-interviewed and are likely to be re-victimised as a result," reads a statement.
The ICCL also said the fact that the Commission believes there are many people with relevant information who have not come forward demonstrates how "the lack of appropriate powers to compel evidence is hindering its ability to uncover the truth".