Under the council's suggested remit, due to be published in June, teachers' capability and misconduct cases would be referred to it. These could include cases where a teacher resigns before capability procedures are completed.
More than 600 teachers have been dismissed under the Government's new fast-track disciplinary procedure, according to research by the National Employers Organisation.
The survey, which covered 116 LEAs for the three school terms, up to spring 1999, found more than 3,000 teachers had been subject to some sort of capability procedures.
Nigel de Gruchy, general secretary of the National Association of Schoolmasters Union of Women Teachers, said incompetence investigations by the GTC woul cut across the function of the employer and bury the council in unnecessary work.
He said: "We already have fasttrack procedures for dealing with this issue. If the GTC gets involved it would be completely overloaded in its first year."
Doug McAvoy, general secretary of the National Union of Teachers, said: "A teacher can be capable in one school and incapable in another. It would also be enormously unfair for a teacher who has decided to leave the profession because they know it is not for them to be dragged before a committee to explain themselves."
Carol Adams, chief executive of the GTC, said the council had no intention of intervening in all capability cases.
"The council will have the power to come in when all the local employment procedures have been exhausted and a teacher has been dismissed. Or in some cases where a teacher resigns and we feel the situation is sufficently serious."