London, UK - Head teachers should allow imams, rabbis and priests to offer religious instruction to pupils in all state schools, teachers' leaders have said.
The National Union of Teachers (NUT) said the move would be a way to reunite divided communities.
The NUT said parents had a right to have specific schooling in their own faith, if that was what they wanted.
But the Church of England disagreed, saying: "Religious instruction belongs with the religious institutions."
'Not about indoctrination'
A Church of England spokesman said: "It is for religions to teach their faith to people; it is for schools to teach about religion.
"Faith schools are not about indoctrinating children in a particular faith."
He added: "Church schools are generally welcomed by parents, which explains why they tend to be over-subscribed."
But the NUT said having children taught at different faith-based schools had led to community breakdown in some areas.
Offering pupils some instruction in their own faith could reduce the demand for faith schools, said NUT General Secretary Steve Sinnott.
'Real benefits'
It could be devised in response to parental demand and would be provided over and above the religious education already included in the curriculum.
Speaking to reporters at the union's annual conference in Manchester, Mr Sinnott said the post-1960s immigration from Southern Asia meant many more Muslim and Hindu youngsters were growing up in Britain.
He said: "This had led some people to reflect whether the development of faith schools was something which should be supported in a national context."
The real concern is that youngsters from different backgrounds needed to be educated together, he added.
"This is more than simple religious education, it's religious instruction.
"There would be real benefits to all our communities and to youngsters if we can find a space for parents who are Roman Catholic, parents who are Church of England, parents who are Jewish, parents who are Muslim for them to have space for some religious instruction.
"In that way we could keep cohesion within communities."
Mr Sinnott acknowledged the plan would require a "significant rearrangement" of the curriculum but insisted it was not "unworkable".
Consequences
"What I am saying is not easy with the curriculum demands of all schools. We could have imams coming in or local rabbis or local priests."
He added: "In some circumstances we might meet it by some after-school provision. This is not something a school should play with, it's not something a school should create as a second tier of responsibility."
"If we did that we could create a drop in support for the initiative in the community," he added.
He said the consequences of not adopting the measures would be more faith schools and more divisions between youngsters of different backgrounds.
The suggestion comes from a policy document expected to be adopted at the union's conference later on Monday.
But John Dunford, general secretary of the Association of School and College Leaders, said: "This plan could compound the problem if the people coming into schools were offering extreme views.
"How would you have any control over what was being taught in your school?"
And Keith Porteous Wood, executive director of the National Secular Society, said "indoctrination has no place in schools."
He said: "Schools providing an almost unlimited variety of religious instruction possibilities is divisive and a waste of time that should be better spent on lessons.
No obligation
"If it is allowed, it will be the zealots who will be imposing their will on everyone else.
"It should be up to parents, if they wish, to indoctrinate their children about religion, but this should not be in our schools."
The NUT's statement came as delegates prepared to debate calls for faith schools to be abolished. However, that debate missed its conference slot and will not now be heard.
Mr Sinnott said abolition was not the NUT's policy, but he did want to see fewer faith schools opening.
He stressed that no pupils would be forced to have any religious instruction.
Faith schooling is an issue that has divided teachers for some time, with calls for their creation and abolition often debated at teaching union conferences.
But ministers are unlikely to accede to demands for them to be scrapped because they are popular with parents - partly because they tend to achieve good results.