Minister for Children and Youth Affairs Katherine Zappone has said that money will not be the most relevant consideration when a final decision is taken on what will happen at the site of the former mother and baby home in Tuam, Co Galway.
A mass grave of babies and children was discovered earlier this year at the site of home, which was run by the Sisters of the Bon Secours.
A technical report being considered by Cabinet lists five options for the Tuam site.
They include making the site a memorial and suspending further investigative work.
Another option would see a full forensic and archaeological excavation of all the grounds once occupied by the home, which includes a playground and a carpark.
The costs involve range from €100,000 to €5 million.
The expert technical group report has warned that it will be impossible to get DNA identification of infants and young juveniles without samples from living relatives.
It found too that even then identification will be extremely difficult and will depend on the quality of the remains recovered.
The group also highlighted that DNA testing can itself destroy the samples recovered.
"While this may be acceptable when dealing with, eg, whole skeletons or significant intact portions, it is far less satisfactory when being used to identify individual fragments of co-mingled remains which are effectively destroyed as they are 'individualised'."
The Tuam home operated from 1925 to 1961.
A number of the samples are likely to date from the 1950s, according to the commission that investigated it.
Galway County Council will now oversee a consultation on this report, which will be completed within three months. Following this, the Government will then take a final decision.
An inquiry was ordered after massive national and international focus on the story of the Sisters of the Bon Secours in Tuam, where the remains of 796 infants are believed to be buried.
Outside of Tuam, three other mother and baby homes have little angels plots believed to hold the remains of another 3,200 babies and infants.
They are Sean Ross Abbey, Tipperary - where the story of Philomena Lee began - Bessborough, Co Cork, and Castlepollard, Co Westmeath.
Infant mortality rates ranged from 30-50% in some of the homes in the 1930s and 1940s.
Minister Zappone said that she fully respects the sincere, diverse views on how this sensitive issue might be addressed.
She also said said she is deeply sorry that details of the technical report were revealed through the media.
Speaking on RTÉ’s News at One, Ms Zappone said she is aware that the report contains some distressing information and the issue of DNA testing was a particularly important one for people to understand.
"It's more technically difficult to identify remains of children under two. It's more difficult to identify remains in the context of this site because some of them have mixed together," said Ms Zappone.
"I understand again from a technical perspective, that when there is an effort to do some DNA sampling on remains, in that process, you can destroy them.
"So these are the things that ... people have to make decisions in relation to whether that's something that they would want."