A Government backbencher has abstained on votes on the draft terms of reference of the Commission of Investigation into Mother and Baby Homes and Related Matters.
Tánaiste Joan Burton described Labour TD Anne Ferris' differences with the Government over its draft order as a "slight" one.
Ms Ferris, who spent her first days in a mother-and-baby home, criticised the lack of objectivity in the Government's selection of the 14 individual institutions the commission is to investigate.
"This inquiry requires great sensitivity, an open door and a listening ear for all the witnesses to this dark corner of Ireland's past, regardless of the title above the door of the institution where they once lived".
She said the sorrow and cruelty endured by all former residents was equal, and that legislators should not discriminate against some.
"I therefore cannot put my name to this proposal," she said.
Her remarks were greeted with applause in the chamber.
The Labour Party leadership tonight said there is "no question of disciplinary action" against Ms Ferris over her abstention on the two votes.
A spokesperson for Ms Burton said that the party recognises Ms Ferris' concerns with the Government motion "because of her own personal story and appreciates how very difficult this issue has been for her".
Sinn Féin deputy leader Mary Lou McDonald demanded that thousands of excluded survivors, including former residents of Co Wicklow's former Protestant Westbank Orphanage, be added to the commission's remit.
She told Minister for Children James Reilly, who is steering the measure through the Oireachtas, that if all these victims and survivors represent an experience of second class citizenship, then those he "chose to exclude are now doubly hurt as second class victims".
She said it was important to identify those who bore criminal responsibility for abuse of women and children, and argued that reparations where necessary in the service of justice.
Ms McDonald said: "We're not satisfied with the commission's terms of reference, not least because it will surely and by design exclude from its remit and consideration literally thousands of victims of human rights violations.
"There's no guarantee here for the Magdalene women previously and wrongly denied the right to a full Commission of Investigation into their particular institutional experience; no guarantee for the illegally adopted or fostered or boarded out children whose very worst experiences may well fall outside the express terms of this commission's remit."
Labour backbencher Robert Dowds sought clarification from the minister.
He said people who had been in institutions not listed by the Draft Order on the terms of reference should be told whether it is possible for them to contribute to the commission's work.
"Some representatives of survivors of Protestant institutions want to know whether their stories can be told," said Mr Dowds.
He added that the testimony of survivors of excluded Catholic institutions was no less important.
Richard Boyd Barrett, the adopted son of an unmarried mother, welcomed the State's "belated response" to survivor power and appealed to Minister Reilly "not to fall at the last hurdle".
He urged Mr Reilly to include the full range of bodies responsible for abusing unmarried mothers and their children.
He said a "complete architecture of repression" had worked as "an integrated whole" and that full redress should be given to all who sought it.
Another adoptee, Tánaiste Joan Burton, said Ms Ferris and she had a slight difference over the terms of reference.
She said she had sought legal advice and is confident there will still be scope for former residents of those institutions not specified in the terms of reference to be heard.
The Labour Party leader also emphasised that Temple Hill, in Blackrock, Co Dublin, the Catholic institution from which she was adopted, is not on the list of 14 institutions to be investigated.
Yet she knew many of her "co-graduates" who were going to contribute to the commission.
Replying to the debate, Minister Reilly said he had responded to some legislators' concerns by making a technical amendment to definitively include widows and separated women who lived in the homes in the commission's remit.
The Minister for Children and Youth Affairs said he recognised Ms Ferris' disappointment that the former Westbank Home in Greystones, Co Wicklow is not included but stressed that the decision was "thought out at length and has the support of Government".
The minister sought to assuage doubts by highlighting clause six in the draft terms of reference permitting the commission to recommend further investigations.
He told the House he believed it would allow the commission to hear the stories of those who spent time in orphanages not specified in the terms of reference and to make a further determination to recommend to him what further investigations might take place.