The Labour Parliamentary Party tonight said the Government needs to address the issue of an apology to the Magdalene survivors in the context of honouring and vindicating them.
Labour TDS and Senators said the treatment inflicted on the women was a historical wrong that had to be put right.
The statement follows a meeting which heard widespread criticism of the Government’s handling of the issue.
Minister of State Kathleen Lynch earlier today said that it was her personal view that there should be an apology.
Tánaiste Eamon Gilmore is said to have shared the concerns expressed by TDs and Senators at the meeting.
It found that an estimated 11,500 women passed through ten institutions between 1922 and 1996.
Survivors of the laundries expressed their disappointment and anger yesterday at Taoiseach Enda Kenny's initial response to the report.
Earlier in the Dáil, Mr Kenny promised that a process to bring reconciliation and closure to survivors will be put in place.
Mr Kenny said that, on behalf of the State, he was sorry they had worked in such harsh conditions.
The Taoiseach said he had read much of the 1,000-page report last night and it had made harrowing reading.
He said it was important to reflect deeply on the findings and make the appropriate response in two weeks.
Fianna Fáil leader Micheál Martin called on the Taoiseach to make an unequivocal apology on behalf of the Government and the State.
Mr Martin also said a dedicated unit should be set up at the Department of Justice to deal with any further matters that may arise, such as redress for the women.
Speaking on behalf of the Technical Group, Mattie McGrath said that one would think from listening to the Taoiseach that the young women went into the laundries voluntarily.
Mr McGrath said that the Government knew what was in that report and he asked why it needed a further two weeks to consider it.
Govt needs to looks at assistance
Earlier, Minister for Justice Alan Shatter said some of the criticism levelled at the Government yesterday came from people who had not read the report.
Mr Shatter said that the Government must now look at what it needs to do to be of assistance to those individuals whose lives were "blighted" by their experiences as residents in the laundries.
Speaking on RTÉ's Morning Ireland, Mr Shatter said the report showed the varied stories of the experiences of the laundries' residents.
"We now know that 35% of the residents of the laundries were there for three months or less, over 60% for less than a year," he said.
"Many of the stories we have heard in recent years relate to individuals who were residents in the laundries for very many years.
"What Government now needs to do is reflect on all the information that is now available, what can be done to be of help to people whose lives have been blighted by long stays in the laundries.
"These are issues that require careful consideration in the context of how we move forward."
When asked whether it was wrong for the State to collude in the enslavement of children and women, the minister said that he did not want to use that type of language.
He said that it was absolutely clear that the laundries were cold and harsh environments.
Sinn Féin TD Mary Lou McDonald again called on the Taoiseach to offer a full apology on behalf of the State.
Speaking on the same programme, Ms McDonald said the issue of redress for victims will also have to be looked at.
She said: "The report clearly states that there was substantial State involvement in the running of the Magdalene Laundries.
"We knew this before the report, but we have it confirmed in the McAleese report, so there is a liability on the State. That is just the factual position."
UN committee member calls for compensation
A leading member of the UN Committee Against Torture has said the Government should compensate the survivors of the laundries.
Felice Gaer welcomed the State's acknowledgement that it had responsibility for the laundries and that there were far more women who were sent there involuntarily than the Government had previously admitted.
Ms Gaer is vice-chair of the UN Committee on Torture, whose calls for an independent inquiry into the laundries prompted the Government to commission the report.
Speaking on RTÉ's Morning Ireland, she said the Government had an obligation to provide redress to the surviving victims.
The committee, which was chaired by Dr Martin McAleese, also reported that coroners do not appear to have been notified of deaths in the laundries for some years leading up to 1996.
The inquiry into State involvement with the laundries said that end-of-life issues relating to the 879 women who died in the institutions since 1922 are of central importance to its work.
The report recalls that the 1962 Coroner's Act made it obligatory to report a death to a coroner where there was a doubt as to its cause.
It noted that GPs were forbidden to certify a death if it was sudden, unexpected, suspicious or unnatural.
Instead, they were obliged to notify the coroner for the district in which the death occurred.
But the committee said that from the limited information available to it, which relates to the latter part of the period it was investigating, it appears there were no such notifications of deaths in the laundries.
The committee said the obligation to notify the coroner also applied to undertakers or any person in charge of an institution or premises where the person who died was residing at the time of their death.
The coroner decides whether the death can be certified without further action, whether a post mortem is required, or whether a post mortem and inquest are required.
Approximately 8% of the women and girls who entered eight laundries between 1922 and 1996 died in them.