"The Ministry of Education and NZEI are currently in negotiation through collective bargaining around pay increases. Over recent years this process has led to increases of up to 1.5 percent each year," she said.
But the support staff are paid out of the schools' operational grants, which were increased in last week's Budget by only 1.3 per cent from next January, or 4 per cent for about one-sixth of school students who are considered at risk of poor outcomes.
Stuart said the operational grants also had to pay for essential costs such as building maintenance and toilet paper, so principals could be forced to cut teacher aide hours to meet other cost increases.
"I want to be able to pay my staff more," the principals said in their open letter.
"But the Government's freeze on school funding in 2017 means any increase the ministry offers support staff as a result of these negotiations will force me to either cut teacher aides' hours to afford a higher pay rate, or to cut other learning resources.
"The only solution is for the Government to offer support staff a fair pay settlement that's also funded so schools and kids aren't forced to pay the cost of it."
NZEI said 70 per cent of the 20,000 support staff earned below the "living wage" of $20.20 an hour.
Some office staff are paid above that rate, but most teacher aides earn between $15.68 and $17.18 an hour.
Principals Federation president Whetu Cormick, who signed the open letter, said some schools such as his own Bathgate Park School in Dunedin paid all their staff at least the living wage. But most schools could not afford to pay more without reducing hours.
"I'm sure that they will cut hours, because people need to have [pay] increments," he said.
"I'm on leave from my school this year but I keep in touch and I'm worried about my own budget.
"Sometimes you can work it out by attrition if a child leaves so the teacher aide is reduced and they can understand that, but to take hours away to cut costs is just an awful thing and I'm always reluctant because we value those people.
"I would hazard that a number of schools would be having to reconsider their options after the Budget."
Stuart said the 1.3 per cent increase in the school's operational grant was less than the inflation rate of 2.2 per cent in the year to March.
"Analysis of the Budget by Victoria University and the NZ Institute of Economic Research shows that real, per child funding for education is dropping by 1.6 per cent this year, and the Government is budgeting for a major decrease over the next few years," she said.
But Kaye said the operational grant increased by 16 per cent between 2010 and 2016, when inflation was only 11.1 per cent and school rolls increased by 3.1 per cent.
"This means that boards of trustees have been resourced to be able to support pay increases," she said.
"Pay increases are wider than just operational grants. For example, we have the Funding Review currently taking place which is looking at potential changes to the way schools are funded.
"Discussions are also taking place around pay equity."
