The council's "cabinet", the convener's committee, met last week and took what it describes as "the rather unusual step" of making its concerns public.
Ivor Sutherland, the GTC's registrar, has written to the Scottish Office to protest that assistants "should have no involvement whatsoever" in the teaching of reading or maths.
The introduction of a new group of "paraprofessionals" was one of the Government's flagship announcements in the wake of the Treasury's comprehensive spending review in July. The Scottish Office has committed Pounds 66 million over three years to allow local authorities to hire the assistants, who would be at the centre of the early intervention drive as well as relieving teachers of some non-teaching burdens.
But the GTC, which is the Government's principal adviser on the supply, training and qualifications of teachers, clearly senses a quasi-educational role that would be at odds with its remit to enhance professionalism in teaching. It complains it was ignored when the plans were drawn up.
Brian Wilson, the previous Education Minister, said the work of assistants would include "support for basic skills such as literacy and numeracy" alongside administrative tasks and general supervision of pupils. "They will not be teachers and they will not replace teachers," Mr Wilson said, and would remain "under the direction of professional teachers".
But the GTC remains "seriously concerned about some of the duties which are apparently to be allocated to classroom assistants with particular reference to literacy and numeracy".
"Classroom assistants should not be seen as trainee or pupil teachers, " Mr Sutherland says.