The Government has pledged to survey parents of pre-school children in the coming weeks to see if the Catholic Church should relinquish control of some schools.
If there is demand for more diversity, the Department of Education said it intends to work with the church and school to organise a transfer.
The surveys are part of the Action Plan for Education 2018 report and will mark the first time that parents of pre-school children are consulted about school patronage.
Fianna Fáil Spokesperson on Education Thomas Byrne TD has expressed his disappointment following the publication of the Action Plan for Education 2018, however.
Deputy Byrne said: “Minister Bruton had an opportunity to deal with some of the fundamental problems facing the education system through this Action Plan.
"However he has failed to do so, as is evident by the fact that it contains no meaningful proposals to deal with the ongoing teacher shortage crisis.
“There have been an unprecedented number of announcements made by Minister Bruton but little in the way of actual delivery. The School Admissions Bill has been announced on at least five different occasions, but there has been no action on any contentious parts of the issue. It’s high-time Minister Bruton actually advanced this issue instead of making the same announcement again and again.
“The Action Plan also fails to deal with the teacher shortage crisis. There is no pathway set out for pay equality for new entrants and little in the way of incentives to encourage new teachers to stay in Ireland once they complete their training.
"Minister Bruton needs to recognise that he will be unable to make the proposals contained in his Action Plan a reality if there are no teachers on the ground to implement it.
“We need to see more action and less spin from Minister Bruton.”