The Government has engaged in meetings with survivors of residential abuse who have been mounting a hunger strike protest outside Leinster House for nearly eight weeks.
Tánaiste Simon Harris said Minister for Education Helen McEntee and Taoiseach Micheál Martin have met with the protesters twice, most recently on 29 October.
The Government wants to see the matter resolved, he said, adding that a mediator met with the group yesterday.
The matter was raised in the Dáil by Sinn Féin TD Darren O'Rourke.
He said the four protesters - Miriam Moriarity Owens, Mary Donovan, Mary Dunleavy Green and Maurice Patton O'Connell - are on the 47th day of their hunger strike and their health continues to deteriorate.
He said it is a very serious situation but they are "cautiously hopeful" after a meeting yesterday with the mediator.
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However, Deputy O'Rourke said they have nothing in writing about their demands for a State contributory pension and a Health Amendment Act (HAA) medical card being agreed by Government.
He said the Government had previously voted against the provision of those two things and he asked the Tánaiste to give them a "written commitment today" that he would meet their demands.
Mr Harris said it was a sensitive matter that the Government wants to see resolved, adding that he hoped it could be resolved quickly.
He said he would seek an update from the mediator today.
He also said daily medical assistance is being made available to the protesters.
The four protestors who say they have been surviving on water, electrolyte tablets, tea and coffee have been moving between the front of Leinster House and to a large tent they have been staying in adjacent to the Department of Agriculture.
Speaking there today 76-year-old Mary Dunlevy Greene who spent time as a child in Mount St Vincents on O'Connell Avenue in Limerick said their demands are modest and they are hoping for progress.
"We are looking for the HMAC card and the contributory pension. It's not a lot. The difference in the pension is €28 a week and there are only 4,000 survivors in the country.
"We are carrying on with the strike every day and hopeful progress is imminent. As far as we're concerned so far we have been denied til we die."
She said there is a responsibility on the State because of its past actions.
"The State put us in industrial schools and we were incarcerated through the courts."
She also said they have been attended to by medical personnel and paramedics on different occasions over recent weeks.
