The Justice for Magdalenes group has made a submission to the United Nations Committee Against Torture over the Government's planned redress scheme.
The group has said the process should be independent, open and transparent and allow for the right to appeal.
It is also seeking an urgent meeting with Minister for Justice Alan Shatter and will meet with Mr Justice John Quirke on Wednesday.
Mr Justice Quirke was appointed by the Government to advise on how to respond to the McAleese Report.
According to the submission, while the group welcomed the State apology to Magdalene Laundry survivors last month, it was concerned that the women's rights to reparation and redress have not yet been vindicated.
The submission added that the Government has not yet complied with the Committee's June 2011 Recommendation to "ensure that all victims obtain redress and have an enforceable right to compensation, including the means for as full rehabilitation as possible".
The Department of Justice has issued a statement in response.
It said Mr Justice Quirke will examine how the Government might best provide supports, including health services such as medical cards, psychological and counselling services and other welfare needs for the women who need such supports as a result of their experiences.
"It is important, not only to acknowledge the experiences of many of the women in the Laundries, but also to look at addressing their future needs.
"It is especially important to pursue measures that will promote healing, reconciliation and, insofar as possible, provide closure to them."