The Taoiseach says society needs to atone for the treatment of mothers and babies kept in institutions.
It comes after the latest report into burials at Mother and Baby Homes was published.
The investigation was unable to find where 900 children who died at Bessborough in Cork are buried.
While it found residents in Tuam must know more about burial practices there.
Taoiseach Leo Varadkar addressed the report in the Dáil.
"It happened at a time when infant mortality was very high - few vaccines, no antibiotics, very poor public health and sanitation, huge numbers of people living at close quarters in congregation settings, said Mr Varadkar.
"However, none of that excuses the indignity in the way in which these babies were treated in death.
"As a society, we inherit a deep shame for what was done back then and we must now endeavour to learn, to atone and to put things right."