Leo Varadkar, meanwhile, has said the Government cannot ignore the public's concerns
The Children's Minister has said she wants the new National Maternity Hospital to be owned by the State.
Katherine Zappone has also called for watertight assurances around the clinical independence of the hospital.
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.
Health Minister Simon Harris has been given a month to come up with ideas about the ownership of the hospital.
Katherine Zappone earlier weighed in on the ownership debate.
She said: "My preference is that the State has ownership in relation to the National Maternity Hospital. In terms of how that happens, I think it's important to provide the Minister with the time to explore."
Leo Varadkar, meanwhile, says he has been struck by the amount of people who have contacted him expressing a real concern about a religious order owning a new public hospital.
"I don't think we can ignore them," he said. "I think as the Government we have to listen to that, and I think Minister Harris has listened to that.
"It seems to be that the majority of people in Ireland don't believe that public hospitals built in the 21st century should continue to be owned by religious orders."
The Dáil this evening passed a private members' motion calling for a guarantee that the new hospital will be built on the St Vincent’s campus "as quickly as possible" and "remain entirely in public ownership".
The Sinn Féin motion also calls for a legal guarantee of full clinical independence.
Sinn Féin's health spokesperson Louise O’Reilly said: “With the passing of this motion, we have seen a major victory for women’s health in this state.
“It is now up to the Government to stand by their commitment made here tonight and I will be following up with the Minister to ensue implementation of these initiatives in the coming days.”