Health Minister Simon Harris has been compared to a 'rabbit caught in the headlights' over his handling of the National Maternity Hospital.
Fianna Fáil claims the Government should have acted more quickly to deal with concerns about its ownership.
The controversy erupted last month after it emerged the St Vincent's Healthcare Group - which is controlled by the Sisters of Charity - will own the new National Maternity Hospital, which is to be located on a site on the St Vincent's Hospital campus in South Dublin.
Enda Kenny is insisting that the hospital will have clinical independence, and that its religious owners could not control the board.
He has given Simon Harris a month to re-examine the ownership issue.
Fianna Fáil leader Michéal Martin, however, says that should have happened sooner.
Speaking in the Dáil, he said: "[Minister Harris] rushed out saying he was going to write to the HSE to seek clarification on the deal. When in doubt, the ministers write to the HSE now - as if he knew nothing about it.
"A rabbit caught in headlines, because the furore that developed as a result of the revelations seemed to catch him by surprise."
Government Chief Whip Regina Doherty has said she is not at peace with the Sisters of Charity owning the new facility.
She told Newstalk Drive: "What I want to see - and what Government's aim is - is to ensure that we will have a clinically and financially independent hospital, that is funded by the State and governed by the laws of this land."
Independent TD Mattie McGrath, meanwhile, claims the ownership of the new hospital is 'no big issue'.
Also speaking on Newstalk Drive, he suggested it is actually happy that the religious group will own the new hospital.
He argued: "They did a lot of good work over the years.
"[Mediator Kieran Mulvey] is happy, and the likes of [National Maternity Hospital Master] Rhona Mahony are happy - so where's the big issue?
"There's an attack on the Sisters here which is silly as far as I'm concerned. It's pedantic, and it's not that big an issue."
Speaking in the Dáil earlier, Mr Kenny said: "We cannot equivocate about having the very best facilities available for expectant mothers, [and] co-location with an appropriate hospital that can provide expert attention for them if they need that."
Fianna Fáil Health Spokesperson Billy Kelleher, meanwhile, says the hospital needs to be built - but added it has to be done right.
Speaking to reporters, he observed: "I think everyone is in agreement that we need to see this facility built, but we also have ensure that the State's investment is protected.
"I think it's part of a broader debate about the whole area of divesting, whereby the State can ensure it retains an ownership, or a say, or a lean, or a charge on the State's investment in those types of hospital facilities."
