A Magdalene support group has said that most of the women who worked in the laundries will be unable to meet with the Taoiseach and Tánaiste as they cannot be publicly identified.
Tánaiste Eamon Gilmore this morning said both he and Taoiseach Enda Kenny would meet representatives of the Magdalene survivors next week.
Mr Gilmore said they intended to have a "direct discussion" with the women about what their needs are and about how the Government should respond to the report into State involvement in the Magdalene Laundries.
However, Dr Katherine O'Donnell of Justice for Magdalenes said many of the woman still operated under a "level of stigma, silence and shame", especially in the absence of a Government apology.
She said the generosity and kindness of Mr Kenny and Mr Gilmore was not in doubt.
What was needed, she said, was an apology that acknowledged the woman had been done wrong and the State had failed them.
Dr O'Donnell said there was a number of interesting parliamentary questions facing the Taoiseach, about whether he heard any formal or informal legal advice before he responded to Martin McAleese's report in the Dáil chamber.
Speaking on RTÉ's Morning Ireland, Mr Gilmore said: "These women have suffered. What they endured was wrong, what happened in this country over those decades was appalling and this Government has heard these women."
Mr Gilmore said he would go back to his Cabinet colleagues after the meeting and they would decide on the response.
"We are going to do the right thing," he said.
Mr Gilmore said someone from his department would be in touch with the women today.
Asked why no apology was forthcoming in the Dáil, Mr Gilmore said the Government took the decision to publish the report immediately and the time needed to consider a response was not there.
He said the Taoiseach had already said "sorry" and added that they would communicate that directly with the women at the meeting.
Meanwhile, the Human Rights Commissioner of the Strasbourg-based human rights organisation the Council of Europe has called on the Government to issue a State apology to the victims of the Magdalene laundry regime.
Nils Muižnieks issued a statement via Twitter saying: "Women victims of forced labor in Magdalene laundries in Ireland & their descendants deserve State apologies and restorative measures."
The role of the Commissioner is an independent, non-judicial institution of the Council of Europe, which is charged with promoting awareness of, and respect for, human rights in the 47 member States.