The number of children attending multi-denominational schools has increased by almost 30 per cent in the last six years, according to new figures compiled by the Department of Education.
There are now 3,578 pupils receiving their education in a multi-denominational school, compared to 2,765 in 1994.
The number of such schools in the same period has risen from 14 to 23.
The Department said the most recent information indicated that 10 new multi-denominational schools were currently in the planning stage, mainly outside Dublin.
The Minister for Education and Science, Dr Woods, said further growth in the sector was anticipated.
The representative body for such schools - Educate Together - said the figures underestimated the current demand.
"The multi-denominational schools are having to turn away pupils every year because we simply do not have enough places for them," said Ms Deirdre O'Donoghue, co-ordinator of Educate Together.
She said one multi-denominational school in Glasnevin, Co Dublin, had to turn away the equivalent of three junior-infant classes last year because of insufficient places. According to a Dail reply from Dr Woods, recent changes in the purchase of school sites had been "of significant benefit to multi-denominational schools".
Under the new arrangements the Department of Education and Science buys a site for a school, rather than the patrons, which in most cases would have been the Catholic church.
The changes mean parents interested in setting up a multi-denominational school have to come up with only minimal finance to get the project off the ground.
However, Ms O'Donoghue said the current regulations, where the Department grants only temporary recognition to multi-denominational schools, mean they do not qualify for maximum funding in their first year of operation.
"It means that by the time the next year rolls around there is an emergency situation," she said.
Dr Woods said he would soon be "responding positively" to a request for more funding from Educate Together, which is financed by its member schools and the State.