A protest is also planned for Thursday
A petition calling on the Department of Health to block the Sisters of Charity from becoming sole owners of the new National Maternity Hospital is nearing 50,000 signatures.
This is far higher than its original target of 30,000.
The Sisters of Charity were party to a €128m redress scheme with the State in 2002 for child abuse, which took place at its industrial schools.
A report from the Comptroller and Auditor General (C&AG) in December 2016 shows that the Sisters of Charity offered €5m towards the redress scheme - but have only paid €2m.
The same report found the religious group had more than €12m in property assets around the country, which were transferred to Dublin City Council, St Vincent de Paul, the South Eastern Health Board and others as part of the 2002 deal.
Emily Duffy, a spokesperson for the Uplift group who started the petition, said: "This is an issue that people in Ireland are clearly outraged about.
"It's rare we see a petition go viral so rapidly, and it shows that people are deeply troubled by the State's utter disregard for the many victims of abuse which took place in institutions run by orders such as the Sisters of Charity."
"At a time where the Government claims it won’t be able to expand the redress scheme because of huge financial implications for the State - the refusal of the Sisters of Charity to pay their fair share is even more offensive and damaging to survivors and their families."
Health Minister Simon Harris says the new National Maternity Hospital will have full clinical, operational, financial and budgetary independence, free of any religious or ethnic influence.
The Department of Health said: "This independence will be assured by the reserved powers which are set out in the agreement and which will be copperfastened by the golden share which will be held by the Minister for Health."
But People Before Profit TD Bríd Smith has called for a special Dáil debate on the decision.
Ms Smith said: "This decision is an insult to those victims of church abuse who went to the redress scheme and who know the foot dragging and contempt this order has shown over the last decades in relation to paying up for their past crimes.
"But it’s also an insult to the women of this country today who are demanding a repeal of the Eighth Amendment and the right to choose. Despite reassurances they know that religious run hospitals will place road blocks on their rights if it contravenes their religious beliefs.
"How can independence be guaranteed when the announcement states the hospital is been 'handed over to the order?'
"Telling us that the order has no role in the day to day running of the facility is not reassuring if there are other avenues to enforce its beliefs on the operations and workings of the hospital and the services it provides. These questions need to be answered in the Dáil."
Meanwhile the Workers' Party have organised a demonstration to protest the decision at the Department of Health in Dublin at 1.00pm on April 20th.
Social Protection Minister Leo Varadkar told Newstalk Drive on Tuesday that he was sure Minister Harris would clarify the ownership issue: "The land there is owned by the Sisters of Charity, so I guess it would have been anticipated that they would have continued to own their own land but that perhaps the building would belong to the board of Holles Street.
"But of course the decision now has been made not to have a board of Holles Street and to merge the two boards."
"I've only seen what I've seen in the media today, and I'm sure the Minister for Health will clarify it in due course".
"I think it's important that is clarified, but like I say I'm sure Simon Harris will do that".