Leo Varadkar said while individual doctors, nurses or midwives could opt out of performing procedures on conscience grounds, entire institutions will not have that option.
Mr Varadkar was addressing concerns about surgical abortions raised in the Dail by Solidarity-People Before Profit TD Mick Barry.
The government is drafting legislation that will allow for any woman to request an abortion up to 12 weeks, subject to a cooling off period, and will allow abortion in extreme cases between 12 and 24 weeks.
It comes after citizens last month voted two-to-one in a historic referendum to repeal the state's constitutional ban on abortions.
The Taoiseach said the legislation would follow the model of the Protection of Life During Pregnancy Act 2013, which allowed for terminations in extreme medical circumstances, and allow individual medics to opt out.
"It will not, however, be possible for publicly funded hospitals, no matter who their patron or owner is, to opt of providing these necessary services which will be legal in this state once this legislation is passed by the Dail and Seanad," he added.
"I'm happy to give you that assurance."
Mr Varadkar added: "That legislation will allow individuals to opt out based on their consciences or their religious convictions but will not allow institutions to do so.
"So just as is the case now in the legislation for the Protection of Life During Pregnancy Act 2013, hospitals like for example Holles Street, which is a Catholic voluntary ethos hospital, the Mater, St Vincent's and others will be required and will be expected to carry out any procedure that is legal in this state and that is the model we will follow."
