Larry Flanagan, the union’s general secretary, has written to some councils that he said were being “inflexible” in ignoring guidance from education secretary Mike Russell in the face of teachers’ concerns.
Mr Russell said last year that schools could postpone the new Higher, which is due to be rolled out next year, if teachers needed more time to prepare.
Authorities risked the lodging of “professional grievances” and perhaps co-ordinated disputes at schools if they refused to comply, Mr Flanagan said. He reiterated in his letter to councils that the Scottish government had accepted the “professional discretion” of teachers should determine how the new qualification was implemented.
“This was partly to do with identified issues concerning the timeline for implementation of the new qualification, but primarily it was predicated on the premise that teachers in schools were better placed to assess what would produce the best option for their pupils than an external body dictating a particular position,” he said.
“To date this seems to have encouraged professional dialogue about the issue and in most cases a resolution has been found.
“We are aware, however, that this is not the case everywhere, with some senior management appearing inflexible and even some local authorities seeking to instruct schools to proceed with the new Higher, irrespective of school-based concerns.”
The EIS considered such an approach as incompatible with the national position set out by Mr Russell and would advise members accordingly, he added. “This may result in a series of professional grievances being taken out and even escalation to the declaration of a dispute at school or local authority level.”
A spokeswoman for the Scottish government said: “We have made clear that the most natural progression is from National Qualifications to the new Higher and have put in place additional support – including £5 million and an extra in-service day for secondary teachers – to assist.”
Local government organisation Cosla said it was “unhelpful” for the EIS to second-guess councils’ decisions.