In April, Northern Ireland's secretary of state published a plan for a budget to be imposed if the Stormont parties could not reach a deal.
The indicative figures included a 2.5% cut to education.
At the time, the group of more than 40 principals in schools in the Belfast area called the proposals "totally unacceptable".
They sent a letter to parents, the Department of Education, the Education Authority and the secretary of state saying they could not impose the cuts "without seriously compromising their children's education".
On Tuesday, they went to a meeting of Belfast City Council to ask for support in fighting the cuts.
Lord Mayor Alderman Brian Kingston has now agreed to write to the secretary of state, MLAs and MPs.
Damian O'Neill, principal of the Good Shepherd Primary School in Dunmurry, told the BBC's Good Morning Ulster programme the principals did not know where else to turn.
"They (Belfast City Council) are the only elected body at the minute who we could reach out to.
"It's very, very important for us as principals that we see the best-possible outcomes for our children.
"But the circumstances at the minute would suggest to me that we won't be able to do that."
Belfast City Council has backed a group of principals who say they will refuse to make cuts to school budgets.