The Irish National Teachers' Organisation (INTO) said that a protest at plans for an Education and Skills Authority - to replace the five education boards - would be "extremely divisive" and an "unnessary diversion".
The union's northern secretary Frank Bunting spoke out after it emerged that the Church is poised to call on around 400,000 parishioners to object to the outcome of the Government's Review of Public Administration, according to today's Irish News.
Letters of objection are being prepared which parishioners will be asked to sign and send to Government.
Under the Government's plans, the Council for Catholic Maintained Schools (CCMS) will be relieved of its administrative duties and reduced to an advisory role.
The bishops claimed that this poses a serious threat to the right of parents to choose a Catholic schooling for their children. The Church's campaign was due to be launched at the weekend but was put on hold after the bishops received a letter from Education Minister Maria Eagle. It is understood the campaign will restart should the RPA proposals proceed as planned.
Mr Bunting said: "We believed that the Church shared the objective of the Government and all of the political parties in Northern Ireland that the way forward involved a shared future in education and other parts of life.
"INTO, representing the vast majority of teachers in the Catholic sector, believes that the fears of the bishops are misplaced. They should have more confidence in their teachers and governors.
"INTO, representing the vast majority of teachers in the Catholic sector, believes that the fears of the bishops are misplaced. They should have more confidence in their teachers and governors.
"We are coming out of such a traumatic period of violence and there is also evidence of deep seeded sectarianism.
"We need to take much bolder and challenging steps rather than create unnecessary division.
"The bishops should have more confidence in what people can do if they work together.
"CCMS served a role and I think it has come to a natural end. We need a single employing authority for all teachers in Northern Ireland."
A spokesman for the Catholic Church said that the Catholic Bishops of Northern Ireland were "very concerned" about the impact of the RPA. "Following clarification from Ms Eagle and the Department of Education it has been decided to suspend the proposed initiative."