Virginia’s tepid economy is hampering efforts in the state’s largest school system to give public school teachers the salary increases they have been demanding for years, officials said Tuesday.

In a letter to be sent to Gov. Terry McAuliffe (D) this week, Fairfax County leaders expressed concern about projections that state funding to the county will fall $4.4 million short of the $16.8 million expected for teacher salaries — a small but key component in what were bitter budget negotiations with county school officials this year.

“It goes without saying that when they adopt their budget, we adopt our budget,” said Supervisor Jeff C. McKay (D-Lee), who introduced a motion to send the letter that was unanimously approved. “There are major financial implications here if this funding does not make its way through to teacher pay.”

The lower amount of expected state funding stems from a $266 million negative balance in Virginia’s fiscal 2016 budget, which McAuliffe’s administration attributed to lower-than-expected payroll and sales-tax receipts.

Fairfax County Public Schools Superintendent Karen Garza. (Shamus Ian Fatzinger/Fairfax County Times )

In May, the governor’s office ordered state agencies to trim spending to address the deficit.

Although the difference in state funding seems relatively paltry in relation to the $2.7 billion school budget, it nonetheless frustrated Fairfax supervisors, who have long complained that state funding for local schools is meager.

Earlier this year, the Board of Supervisors factored in the anticipated state funding to reach an agreement with school officials for teacher raises, part of an effort to keep teachers in the country’s 10th-largest school system from leaving for higher-paying jobs. The county, which funds most of the school budget, also increased residential property taxes by an average of $304 per year in adopting its spending plan for fiscal 2017.

“It would be unfortunate for us to come up short because of the state’s projections,” said Sharon Bulova (D), the board’s chairman, who signed the letter asking the governor to find a way to give the county the full $16.8 million.

The governor’s office said that McAuliffe would look at options to find extra state funding for schools, including new legislation.

“The Governor understands the importance of ensuring that our state employees, teachers and other state-supported public employees receive the pay they deserve for their hard work on behalf of our citizens,” Christina Nuckols, a McAuliffe spokeswoman, said in a statement. “He is committed to working with state lawmakers on this issue.”

Superintendent Karen Garza’s office said it also would work to find a way to fully meet its promise to give teachers $40 million in salary increases.

“However, any decrease in funding from the state has a negative impact on our budget and places a greater financial burden on our county funding partners and our school division to close the gap,” schools spokesman John Torre said.