The union will have a mandate to go on strike again within six months if it looks like the cuts are being reintroduced or the budget is not going to pass.
However, the SNP group’s size means it is unlikely to fail.
Glasgow City Council previously said no teachers in permanent jobs would be made redundant and that savings would come from not filling vacant posts or by reducing staff on temporary contracts.
The local authority said it needed to look at every option to make savings, as the education budget covers more than half the local authority’s direct expenditure
Deputy council leader and city treasurer Richard Bell told BBC News council funding from the Scottish government was “higher than anticipated” when the initial three-year plan was set.
He said the additional funds had allowed the council to take teacher savings off the table but acknowledged there was still work to be done on balancing the books for future years.
He added: “We will have to work very hard with the government to ensure the settlement that we get next year is of a decent size.
“We’ve said to the EIS we will produce a roadmap on how we get to that figure and will be in consultation with them. It will be about adjusting the formula.
“So, we are still working on the financial solution to that but we’ve given them a commitment to take the big teacher savings off the table.”