Teachers in Catholic schools are being urged by their largest union to refuse to use one of their training days as a "Catholic ethos day".
The letter advocates a 'Catholic ethos day' in schools
The Irish National Teachers' Organisation (INTO) said the request by bishops raised issues of equality and the use of resources.
The union said "an edict" had been handed down by the bishops in their letter to school principals.
However, one Catholic bishop said unions did not have to be consulted.
Tony Carlin of the INTO said his union had been contacted by several teachers angry at the development.
"They said they have been asked to set aside one day in this academic year in which to look at the ethos in the school and to take that forward and to see how it is developed in the Catholic school," he said.
"There has been no consultation with INTO," he told the BBC's Good Morning Ulster programme.
"There has been nothing that has come through the recognised negotiating arrangements and therefore we see this as an edict to our members in Catholic schools."
'Letter to principals'
He said the union was concerned at the development, given that schools were already finding it difficult to find time for staff training.
"We cannot get training for members on how to deal with bullying and harassment, on equality of opportunity and we cannot get training for staff on things like their terms of condition and employment.
"Now we are being told that as a priority you must look at the ethos of the school.
"We do not know what message this is sending out, because an ethos is not required in other sectors of education in Northern Ireland."
The letter to principals came after a recommendation from the Consultative Group for Catholic Education.
Bishop Donal McKeown of the Down and Connor diocese confirmed that the bishops had made the request to schools.
He told the BBC: "It came from a group primarily made up of lay teachers who have been working for this past couple of years to say: 'What is a Catholic school and specifically what is a Catholic school in Northern Ireland in this age of secularisation and need for reconciliation'?
"The bishops were simply asked by this group of mainly head teachers if they would write a letter out to schools."
Bishop McKeown said his recollection as a principal was that he did not have to consult teachers' unions about what was involved in staff development.
"Each school, in the context of its own development plan, has to make its own priorities," he said.