Cosla accused the Scottish Secondary Teachers' Association of threatening to "disrupt children's education" because of disagreement with other teaching unions. The council chiefs' body also said teachers had "enjoyed good increases in pay over the last three years" and were not being singled out.
At the weekend, teachers in two separate unions backed moves to resort to industrial action over changes to the profession's pay and conditions.
On Friday the Scottish Secondary Teachers' Association (SSTA) unanimously backed a motion declaring they were prepared to use industrial action.
The following day the National Association of Schoolmasters and Union of Women Teachers (NASUWT) unanimously backed an urgency motion committing the union to industrial action.
Memberships of both unions rejected the latest pay deal offered by council bosses in a ballot of all members.
It means a pay freeze for staff and cuts to supply teachers and conserved salaries as part of 45 million cuts to education.
However, Scotland's biggest teaching union, the EIS, voted to accept the deal with a successful ballot of 56 per cent.
Chris Keates NASUWT general secretary said: "Teachers have been singled out and discriminated against in a deliberate, calculated and unwarranted manner simply to balance the books of the Scottish Government and local authorities.
"Pay and conditions are being worsened on the votes of only a quarter of the teachers in Scotland. Three quarters have been disenfranchised.
"Not only must the Cosla proposals be challenged but the time has come for a root and branch review of the negotiating machinery."
Ann Ballinger, general secretary of the SSTA, said any action would not be strike action but could take the form of a work to rule.