A survey by the Irish Primary Principals Network found that Irish parents would prefer their children to attend State-run primary schools open to all religions rather than church-run schools.
In the Red C survey, 327 parents of children under 15 were given a series of questions about religion in primary education.
They were asked if they would prefer a school managed by and promoting the faith of a particular religion or a school managed by the state with equal status and opportunity for all religions.
In the survey, which was carried out three years ago, they voted three-to-one in favour of the State option.
The poll also showed that parents wanted less time spent on the teaching of religion in primary schools and more time on activities such as PE.
At present, two-and-a-half hours each week is devoted in primary schools to religion.
In apparent contradiction of some of the poll's other findings, 56% of all parents said religious instruction and the preparation for Catholic sacraments should be taught by the class teacher during school hours.