The Taoiseach Enda Kenny is being called on to apologise on behalf of the State to the women and children who resided at mother and baby homes.
Fianna Fáil TD Colm Keaveney says the details emerging about one such home in Tuam in Galway where the bodies of up to 800 babies were buried in a tank amounts to a "scandal".
It comes after the revelations that the remains were buried in a mass grave next to a home for unmarried mothers in Tuam, Co. Galway between 1925 and 1961.
The Tuam Mother and Baby Home was run by the Bons Secours nuns.
The Adoption Rights Alliance group has said it has anecdotal evidence that babies with disabilities or other health issues - which made them unlikely to be adopted overseas - were not cared for properly and were allowed to die.
Deputy Keaveny says the government is refusing to debate what happened there and why, and he believes Enda Kenny should apologise.
He said: "In my hometown there were 800 bodies of Irish citizens resting in a septic tank, and the Government are refusing to facilitate a debate today on this most important issue.
"I'm arguing that the Taoiseach needs to come forward and offer a fulsome apology on behalf of the Irish State to the mothers, and to the children and to the Irish people with respect to this scandal."