St Vincent's Healthcare Group say it is due to "controversy and misinformation"
A review is to be carried out into the status of the new National Maternity Hospital.
The chairman of St Vincent's Healthcare Group, Jimmy Menton, says it is due to "controversy and misinformation" regarding the project.
The Elm Park campus, where the new facility is to be built, is owned by religious group the Sisters of Charity.
Health Minister Simon Harris has come under severe pressure since it emerged that sole ownership will handed to the group once the hospital is built.
The minister had claimed the group would receive no financial gain from the new hospital - and pledged to ensure the facility will remain entirely independent in terms of its clinical, operational, budgetary and financial operations.
An agreement was signed in November 2016 providing for the corporate and clinical governance arrangements for the new maternity hospital.
In a statement, St Vincent's Healthcare Group say: "That agreement was publicly endorsed and welcomed by both the Minister for Health, Deputy Simon Harris, and the Taoiseach, Deputy Enda Kenny, at a press briefing that evening in Government Buildings."
But it adds: "In view of the controversy and misinformation that has arisen in recent times regarding the project, and the views expressed by the Minister for Health and other members of the Oireachtas, the board of St Vincent's Healthcare Group will review the status of the project in light of the current situation.
"Pending this review, the board does not intend to make any further comment."
In response, the Department of Health say Minister Harris outlined his position "very clearly" and remains fully committed to the project.
His department say the minister "is confident that the criteria which he has identified will be met as the project proceeds, subject to planning approval, through the various development stages.
"Further stages of the process involve the minister discharging his duties with various parties by putting in place appropriate legal mechanisms.
"This will include arrangements to secure the State's interest, which apply in all capital projects on voluntary hospital sites to protect the State's investment."
It says the minister himself will formally sanction these arrangements.
The statement from the Department of Health reiterates: "The clinical, operational and financial independence of the new hospital as provided for in the agreement will also be copperfastened in new legal arrangements."
Health correspondent with the Irish Times, Paul Cullen, told Newstalk Drive it appears intervention from Minister Harris has rubbed some people up the wrong way.
"My feeling is that St Vincent's have played hardball right through the negotiations - they're negotiating from a position of strength in that they own the location for the hospital.
"The sentiment even before this, but certainly now, is that they would happily walk away from this - and that would mean that no maternity hospital would be built in the foreseeable future.
"That's how serious this is, and it's also serious for the minister as well because they clearly see that the minister's intervention was an attempt to unpick the agreement that was reached last November".
Earlier, the chair of the Oireachtas Health Committee Dr Micheál Harty said it was not important who owns the hospital, telling the Pat Kenny Show: "I think who owns the hospital is not the issue.
"It is what happens within the hospital that is the issue - and I think there has to be obviously clinical and operational and financial governance within that hospital that has to be independent.
"I think that there needs to clarity [...] if the Sisters of Charity for instance came out and definitively stated that they would not have any ethical involvement in the running of the hospital that would clarify the issue very quickly.
“In relation to the hospital it has to have a secular ethos, it cannot have an ethos that is run by one religious body."
Nearly 80,000 people have signed an online petition against the ownership, and a protest was held outside the Department of Health on Thursday.
There have also been calls for a Dáil debate on the issue.