Six women from the Magdalene Survivors Together group have said they are confident they will receive an apology on behalf of the State from the Taoiseach very soon.
The women were speaking after a three-hour meeting with both Taoiseach Enda Kenny and Tánaiste Eamon Gilmore at Government Buildings this afternoon.
They said they had received a very compassionate response from both men.
A spokesman for the group said they wanted to share their stories with the two men and hoped an apology would be forthcoming.
They said that they were not looking for a private apology today but a public apology on behalf of the State when the Dáil debates the McAleese report next week.
The Taoiseach said the subject of redress was not an issue for today.
The meeting followed the publication of the report into the State's involvement in the Magdalene Laundries.
Both the Justice for Magdalenes advocacy group and the London-based Irish Women's Survivors' Network said earlier that they would not attend the meeting.
Before the meeting, Mr Gilmore said the meeting was taking place because the Government believed the women's story and wanted to do as much as possible to help them.
The Dáil will this week debate a Fianna Fáil motion calling for a full and unqualified apology to the women of the Magdalene Laundries.
The Fianna Fáil party is also calling for the establishment of a dedicated unit within the Department of Justice to co-ordinate the State's response to the McAleese report, including all forms of redress for the survivors.