The dispute at the Holy Cross Catholic girls' school in north Belfast could spread to other schools in the area unless a resolution is found, the Ulster Unionist Party leader has said.
"The scenes at Holy Cross Primary are totally unacceptable and are overshadowing the genuine concerns of Protestants living in interface areas in north Belfast. Until violence ends and dialogue begins these concerns cannot be resolved," Mr David Trimble said. "The present situation is appalling. There is a serious danger that the problems could spread to other schools in the area."
The former first minister said dialogue had failed because some groups would only address one issue and not others, and because of a range of matters - which extend to security, housing and social deprivation.
Speaking on behalf of all the Church of Ireland bishops, the Archbishop of Armagh, Dr Eames, said the dispute could spread and urged all sides to try to reach an accommodation.
"I know there are fears in other schools and I know it's not just a question of one school, there are other parents who are worried today," he said.
"Throughout the Troubles, schools of all denominations have been havens. Children have been secure there. And now to see children sucked into our Troubles in this way is absolutely deplorable. I utterly condemn this sort of action against innocent little children."
The Sinn Fein Education Minister, Mr Martin McGuinness, warned the dispute could only be resolved if unionist and loyalist political leaders spoke out against the violence.
"This situation is affecting young people in both communities, and is deeply damaging to children, not just at Holy Cross but also at [neighbouring Protestant] Wheatfield Primary School," Mr McGuinness said.
He said he would be "absolutely horrified and disgusted" if there was any truth in the allegation that the situation was being manipulated by republicans.
The Catholic Bishop of Down and Connor, Dr Patrick Walsh, called for the protest to stop. "The school must be allowed to function properly and then those people in positions of responsibility must be able to come together," he said.
He refused to instruct parents to take their children to school through an alternative route.
A local Presbyterian minister, the Rev Norman Hamilton, from Ballysillen, has been involved in mediation attempts.
"But it is going to be a longterm process of helping each community to understand the fears of the other," he said.