Edinburgh University's principal, Sir Stewart Sutherland, has warned staff that they may damage students' future careers if they withdraw from examination invigilation.
The local Association of University Teachers has voted not to invigilate from this week.
Sir Stewart said the university would make every effort to ensure the exams proceeded as normally as possible. But there was a risk that some would have to be rearranged or deferred because of the action that went "far beyond" the recommendations of the AUT's national executive.
"I would wish to make it absolutely clear that departments are responsible for the proper conduct of examinations for their students - which at the moment includes invigilation - and that heads of department are responsible for ensuring that this duty is discharged," he said.
Edinburgh's AUT, however, has condemned Sir Stewart's "intemperate language", saying it would be better used to tell the government about the underfunding of higher education.
Alan Walker, president of Edinburgh AUT, said that for historical reasons, staff believed invigilation was undertaken on a voluntary rather than contractual basis.
A general meeting had voted not to invigilate by 74 to 1. This decision was not taken lightly but because of frustration with the impasse in pay negotiations.
In the past, the university had paid non-academics to invigilate, and could do so again, Mr Walker said.