Micheál Martin said Irish governments had invested public funds in facilities like Dublin's St Vincent's Hospital and the Mater Hospital for many years.
He said the state was essentially running the hospitals, not the Church.
Mr Martin, who leads the Fianna Fáil party, made his comments to the Irish broadcaster, RTÉ.
"In my view any area in education or health, where fundamentally the state has made a large investment and continued to make the investment for over 30 or 40 years, when that comes to an end, the utilisation of that facility for those purposes, I think those facilities should then revert to the state," he said.
St Vincent's University Hospital was founded by the Religious Sisters of Charity in Dublin city centre in 1834.
In 1970, it transferred to its current site in Elm Park, Dublin 4, just south of the city centre.
The Religious Sisters of Charity remain as shareholders of the hospital, and it is run according to their philosophy of "human dignity, compassion, justice, quality and advocacy".
The Mater Misericordiae University Hospital was opened in 1861 by the Sisters of Mercy.
It still operates from its original site on Eccles Street in the north side of the city and celebrated its 125th anniversary last year.
The Mater is home to the biggest 24-hour emergency department in the Republic of Ireland.
The Fianna Fáil leader made his remarks about ownership of the institutions during an interview about the discovery of human remains at a Catholic-Church run home in Tuam, County Galway.
Last week, a government-appointed inquiry confirmed "significant quantities" of human remains had been found at the site of the former home for unmarried mothers and their children.
Hospital sites owned by the Catholic Church in the Republic of Ireland should be handed over to the state, the leader of the opposition has said.