Hoping to avoid layoffs and other cuts to the county’s financially strapped school system, Fairfax supervisors on Tuesday agreed to push state lawmakers for more funding for K-12 schools.

The county’s 184,500-student school district is staring at a projected $132 million budget shortfall next year that officials say is due to escalating health insurance costs and higher demands created by a growing student body.

The fiscal problems in the state’s largest school system have led to tensions between school officials and the county government, which funds Fairfax schools and is already planning to direct an extra $34.3 million toward the district next year.

At a board meeting Tuesday, the Fairfax board of supervisors argued that some of the burden in shoring up the school district’s $2.5 billion budget should fall on Richmond.

The board voted to direct the county’s legislative staff to lobby for more funding for early childhood education programs and to push state officials to restore cuts to a teacher salary fund that, during the past two years, have resulted in $10.2 million less for Fairfax schools.

“If we’re going to deal with this budget deficit, part of the solution is to restore something we’ve already cut that the state has acknowledged for many, many years is a necessary source of revenue for the county,” Supervisor Jeff McKay (Lee) said, about the Cost of Competing Adjustment salary fund.

Board Chairman Sharon Bulova said the county will begin pressing for the school funding increases shortly after the General Assembly convenes next month.

In a legislative package passed by the county board Tuesday, Fairfax officials noted that state funding for K-12 schools in Virginia has steadily dropped since 2009 to about $5.3 billion during the current fiscal year. Fairfax County’s current share of state funding is about $387 million.