Demand for places in Educate Together - the multidenominational primary schools - has reached record levels.
Launching the group's three-year plan, its chief executive, Paul Rowe, said demand was escalating for places, and there were calls for the establishment of 50 more schools across the State.
The movement estimates some 400 Educate Together schools will be required to provide choice for parents.
Established 30 years ago by volunteer activists, Educate Together has been remarkably successful. There are now more than 40 such schools in the State, many of them established in the past seven years.
The group is one of the main providers of new schools in rapidly developing areas of population throughout the State.
Mr Rowe said the movement was determined to address the lack of choice in Irish education.
"The fact [ is] that in the vast majority of areas, families in Ireland do not have access to a school that is based on the inclusive principles of the Educate Together model and can only send their children to a school that is faith-based in ethos and management. "
The level of demand and the lack of State initiative in this area raises a fundamental human rights issue for Irish society, he said. "We cannot progress our social space, our education system or indeed any real concept of a knowledge society unless we ensure that all families can access a school in which their social, cultural or religious backgrounds are guaranteed equality of access."
An education system that - through lack of State initiative - introduces an element of compulsion in the area of personal identity infringes on the intellectual rights that must be at the core of education, he said.
