After wrangling with county schools, employees and other groups over spending cuts and higher property taxes, Fairfax County will have a $34 million budget surplus heading into the next fiscal year, county executive Edward J. Long announced this week.

Of that amount, $23 million is being steered to meet adjustments in administrative and other costs, leaving $11.22 million available for “critical, one-time requirements,” Long said in a memo to the county board of supervisors.

Faced with increasing demands for service from the Fairfax school system and other areas of the county, the board of supervisors — which met for the last time Wednesday night before its August recess — will decide in September what it wants to do with the extra cash.

Long counseled prudence, warning the board that the regional economy is still sluggish, demands for service continue to increase and cuts in state spending may lead to fewer tax dollars for Fairfax during the coming year.

“All of these combine to limit flexibility to provide required resources,” Long said in his memo. “In addition, both the County and Schools have experienced many consecutive years of slow revenue growth, and program reductions and further cutbacks without significant programmatic impact are unlikely.”

Long recommended using $3.5 million of the surplus to replace county voting machines. He also suggested reserving $5.75 million that may be needed in 2016 to help with the anticipated opening that year of a new eight-story police headquarters that’s now under design.

With the Fairfax school board seeking $7.6 million for a recently approved plan for full-day Mondays at county elementary schools, the debate over what to do with the surplus money is likely to echo contentious budget hearings earlier this year over school spending.

In hopes of reaching consensus early, county and school officials on Wednesday began joint budget discussions that will last through October, and longer if needed, officials said.

Sharon Bulova, chairman of the board of supervisors, said she has an open mind about the schools’ needs, though she noted that the school system has its own budget surplus this year that “is larger than” the $11.22 million the county has to spend.

“I want to wait to hear what they have to say . . . and what their plans are,” Bulova said. “They have their own challenges and I’m sensitive to that.”