The Government has agreed details for the implementation of the Magdalene redress scheme.
Minister for Justice Alan Shatter said 250 applications had already been processed and around 600 applications have been received to date.
Mr Shatter said he would hope that provisional offers of payments would be made in the next four to six weeks.
Eligible women are entitled to a lump-sum payment of between €11,500 and €100,000, with amounts over €50,000 to be paid by weekly instalments.
Four congregations - The Sisters of Our Lady of Charity, the Mercy Sisters, the Sisters of Charity and the Good Shepherd Sisters - ran Magdalene Laundries.
An estimated 11,500 women passed through ten institutions between 1922 and 1996.
A report by the Inter-Departmental Committee to establish the facts of State involvement with the Magdalene Laundries was published earlier this year.
It found the environment in the laundries was harsh and involved physically demanding work, which produced a traumatic and lasting impact on the girls.
There were many instances of verbal censure, scolding and humiliating put downs.
However, no allegations of sexual abuse were made against the nuns.
The report found that the State was directly involved in the running of the laundries, with just over one quarter of referrals made by or facilitated by the State.
Taoiseach Enda Kenny apologised unreservedly on behalf of the State to the survivors of the laundries earlier this year.
Justice for Magdalenes Research group has said it welcomed the minister's comments, but said is disappointed that the State could not yet deliver on pensions and healthcare benefits.
It said: "We are concerned ... that the State is not yet ready to deliver on the promise of pensions and healthcare benefits, which await the passage of new legislation.
"It is now over four months since the government accepted Justice Quirke's Scheme in principle. We question why the necessary legislation is not already in place to facilitate these additional benefits."
Elsewhere, Labour TD Anne Ferris has called for a mechanism to "claw back" contributions from religious orders towards the payment of redress.
Under the Finance Bill, those who are eligible for redress payments from the Magdalene Laundries listed in the bill will not be obliged to pay taxes on those payments.
While the Wicklow TD welcomed that aspect of the bill, she criticised religious orders, which she said are "not paying their fair share".
Speaking on the second stage of the bill in the Dáil, Ms Ferris said there was an "accounting assumption" in some church-run State-sponsored facilities that pension deficits for staff "would be funded by the State at some point in the future".
She concluded her contribution by calling for an inquiry into past abuses, adding if there was an expectation that the public would take on "an unfair share of the cost of these redress schemes then the Irish people should know why".