Just under 260 completed application forms have been received from survivors of Magdalene Laundries who believe they qualify for the Government's restorative justice package.
The Department of Justice has told RTÉ that 670 forms were issued late last month to women who had responded to an invitation to register an interest in the scheme.
It offers monetary payments ranging from €11,500 to €100,000, along with various other benefits including an enhanced medical card.
There is no time limit to the scheme.
Earlier, Minister for Justice Alan Shatter said he cannot strip the four religious orders who owned the laundries of their charitable status.
It follows their refusal to contribute to the Government's multimillion euro redress scheme for survivors of the institutions.
Magdalene Survivors Together called on the Government to remove the orders' charitable status and to cease State funding in response to their decision.
The orders concerned are the Sisters of Our Lady of Charity, the Sisters of Mercy, the Good Shepherd Sisters and the Religious Sisters of Charity.
The nuns have offered to help the women in other ways, such as caring for about 100 of them in residential settings.
The Government is set to pay between €34.5m and €58m to the Magdalene survivors.
Orders asked to reflect on issue
Taoiseach Enda Kenny and Tánaiste Eamon Gilmore have both called on the orders to reconsider their position.
Mr Kenny said the Government had delivered the redress scheme that the survivors had wanted.
He said that the women did not have time on their side, and they wanted a scheme that was non-litigious and that would not be drawn out.
Sinn Féin President Gerry Adams asked what the Government would do to ensure that the institutions would contribute.
Speaking during Leaders' Questions in the Dáil, Mr Adams said it was "not good enough for the Government to be disappointed" in the orders' decision not to make a contribution.
Speaking on RTÉ's Morning Ireland, Mr Shatter said it was not possible to take legal action against the orders.
He also said the orders continued to carry out charitable work and qualified for charitable status under the law.
Magdalene Survivors Together said it was appalling to think that the Dáil is not in a position to hold the orders to account.
Steven O'Riordan of the group said: "The perpetrators of the crimes and the enormous suffering with which these women have suffered is being made a mockery of by the religious orders.
"We now have a situation whereby the orders who ran these institutions have given the Magdalene women and the Irish people the two fingers."
Magdalene survivor Marina Gambold called on the Taoiseach to act.
She said: "What these religious orders have done is so disrespectful to all the women who were in those laundries.
"They destroyed our lives; they took my human rights away from me. They brought shame and hurt to our country and the Government is just allowing them to insult us like this.
"I thought Enda was better than this. I looked into his eye and I told him my story. He quoted my story the night of the official apology and now our leader allows these nuns to do this?"
Meanwhile, a decision on a redress scheme for the Bethany Homes survivors will be made at the next Cabinet meeting.
The form for the Magdalene Laundries restorative justice package and information about how to complete it is available online.
Intending applicants or their advocates may also write to: The Restorative Justice Implementation Team at Montague Court, Montague Street, Dublin 2.
They may also telephone 01-476 8660 or contact any Citizens Information Centre in the Republic or any Irish diplomatic representation abroad.