Fianna Fáil leader Michéal Martin said the new National Maternity Hospital would have to have clinical independence and should not be compromised.
He was responding to reported comments in The Sunday Times by the Bishop of Elphin Kevin Doran, that the Sisters of Charity will have to obey Catholic Church rules if they become owners of the new National Maternity Hospital.
He said the new hospital had to be free of any religious ethos.
Mr Martin called on the Minister for Health Simon Harris to be fully transparent about the process and the deal that has been made.
Earlier this week, it emerged that the Religious Sisters of Charity was to be given ownership of the €300m taxpayer-funded hospital because it owns the land on which it is to be built.
The new hospital is to be built on the campus of St Vincent's Hospital in Dublin.
Mr Martin said if the taxpayer is investing a large amount of money, then that should be reflected in the ownership of a facility.
He said the offer to buy the site should have been made, and that it was unclear why it was not up for discussion.
When asked if church and State are still too knitted together, he said religious orders in the early years of the State made significant contributions to the country in terms of education and healthcare but when there are substantial amounts of money being invested by the taxpayer in a completely new entity, that investment has to be reflected in the ownership.
Meanwhile, Labour Party leader Brendan Howlin has said that no one should be surprised that a catholic bishop would seek to have the catholic ethos applied to a hospital owned by a catholic religious order.
Speaking at the Labour Party conference in Wexford, Mr Howlin said the hospital must be owned by the State or they should consider another site.
A Fine Gael TD said that Bishop Doran's comments does not change the agreement reached on the independent running of the planned new maternity hospital.
Speaking on RTÉ's The Week In Politics, Colm Brophy said the view of Bishop Doran that a healthcare organisation with a Catholic name has a special responsibility to that church's teachings, will not override the legal agreement reached with the religious order that owns the St Vincent's site.