Angered by an NUT newsletter claiming that signatories to the agreement could not amend the Government's workload proposals, the ATL is to tell the Trades Union Congress that attempts at reconciliation are futile.
Gerald Imison, ATL joint acting general secretary, said: "We will be saying to the TUC don't bother trying to get us back together again because we won't join in."
The association is writing to Doug McAvoy, NUT general secretary, angry at what it sees as an attempt to undermine the unions that have signed up to the deal.
Mr Imison said the NUT's newsletter, sent out to schools this month, was the final straw. He said that claims that signatories could not propose amendments to the agreement were "wholly untrue".
He said: "We will not work with the NUT on anything, except on a case by case basis where it would be in the interests of our members."
Mr McAvoy said the newsletter's offending paragraph was based on what the other unions had said at a TUC meeting. He said: "We were merely re-iterating their position as they had explained it to us."
The NUT's relationship with Unison and the National Association of Schoolmasters Union of Women Teachers is also close to breaking point following its threat not to co-operate with teaching assistants that take classes alone.
A TUC spokeswoman said: "Our role is to bring people together and that is what we will continue to do."