The INTO is seeking the establishment of a forum on religious education in interdenominational schools amid growing evidence that many parents are unhappy with traditional denominational schooling.
Many teachers, the union says, are now beginning to wonder if they alone are responsible for the religious development of a majority of children.
In his first major speech as the new general secretary of the union, Mr John Carr said religious education must reflect the growing diversity of society.
It was often left to teachers to pursue religious education "in the face of less and less clerical involvement in schools at local level and declining parental participation in religious activities", he said.
The INTO has been prompted to table its demand by recent events at the interdenominational gaelscoil in Dunboyne, Co Meath. A mediation team has now been established to examine the case in which a school principal is facing possible dismissal by the board of management.
The INTO wants the new forum to examine a wide range of issues including:
The needs and rights of children in the area of religious education.
Parental rights, obligations and expectations.
The professional rights and obligations of teachers.
The possibility of a national core curriculum in religious education.
Other issues include the implications of legislation for schools, the impact of changing demographics and the experience of other countries.
Mr Carr says little official effort has been made to reflect the growing religious diversity in the school curriculum, in school accommodation and in legislation.
"In this context the INTO calls for the establishment of a major forum on ethos in interdenominational schools representative of all education partners," he said.
Ireland had seen rapid change, and the education system could not and should not remain immune.
However, he said, the freedom of individual teachers to embrace the diversity in the classroom was often severely curtailed.
"This comes at a time when some teachers are reporting that they are finding it increasingly difficult to get local clergy to visit classes in schools, even classes being prepared for the sacraments," Mr Carr said.
"Indeed there is anecdotal evidence to suggest that many local clergy do not view this as a core activity or an essential part of their role."
Teachers, he said, were regularly asked to make alternative arrangements for those who did not wish to avail of a particular religious education. This they did, often in the face of constraints on classroom accommodation and supervision arrangements.