Fairfax County school administrators said yesterday they will ask the school board to seek a 15.5 percent increase in next year's county school budget in anticipation of U.S. budget cuts, salary increases and inflation.

The proposed increase, if approved by the board, could set the stage for a struggle between school officials and the conservative Board of Supervisors, which provides about two-thirds of the school budget. The school system also will be competing with other county agencies expected to ask the board to make up for other federal cutbacks, raising the specter of unpopular tax increases this year.

Though Superintendent Linton Deck said he expected the board to approve the $436.4 million budget, other county officials were less certain.

"If the board approves the superintendent's budget as it is," said board member Gerald A. Fill of the Mount Vernon District, "it's going to make it very difficult for the supervisors to keep a lid on taxes."

"We're going to hold the line on the real estate tax rate," said county board Chairman John F. Herrity. "And I don't foresee any other increases in any other types of taxes. That's pretty well the opinion of the entire board."

"There's probably a considerable amount of justification for the increases ," said county spokesman Edmund L. Castillo. "But . . . there's only a limited amount of money in the pot."

The school administration's proposal calls for a $42.8 million increase in its budget for fiscal year 1983 -- a 10.9 percent increase over this year's budget. Because of federal cuts, the county will be asked to increase its share of total school budget 15.5 percent, or $38.9 million. The county now finances 64 percent of the school budget, but under the new proposal the county would fund almost 67 percent -- or $290,905,600. The board began review of the proposed budget last night and is expected to vote on it in Feburary.

The school administration also proposed increasing the price of school lunches by 10 cents next year to compensate for cutbacks in federal school lunch subsidies. If approved by the school board, the action would boost the cost of elementary meals to 85 cents and secondary school lunches to 95 cents. Since the county does not currently support the cost of the lunch program, the price increase will not have to be approved by the county supervisors.

Compared to Fairfax's 10.9 percent proposed total budget increase, Montgomery County school officials Monday requested about a 1 percent increase in its current budget. Montgomery officials said that figure does not include any increase that may be required to meet possible employe pay raises.

Although Fairfax school officials blame much of their proposed spending increases on federal cuts in school aid, they expect to lose only about 1 percent of their total budget, or $4.74 million, to federal funding cuts this year. Federal aid makes up only about 3 percent of the system's budget.

Deck said the cutbacks coupled with salary increases, inflation and increasing state, local and federal requirements and citizen expectations for better educational services for the handicapped have pushed the budget up. Despite continuing declining enrollments in the schools, this year's budget includes 86 new positions, many of them in the area of special education.

Of the $42.8 million proposed increase, $15.3 million is allotted to give school employes the 5 percent pay raise tentatively approved by the school board and board of supervisors two months ago. Employe salaries and benefits consume about 85 percent of the entire proposed budget.

Other areas in which the proposed increase would be spent include:

* About $1 million for expanding classroom computer equipment and classes in high schools and elementary schools, as well as for increasing the capacity of the computer system used in the routine operation of the nation's 11th largest school system.

"There's no way we can expect our students to function in the 21st century without training in the basics of dealing with computers," Deck said. He also said he will request expanding the program to all elementary schools during the next few years.

* About $1.8 million for replacement of supplies, classroom equipment, maps and globes.

* About $404,000 for 60 instructional aides to provide special help for students.

* About $2.7 million for 70 new buses and other school vehicles.

* Recruitment incentives costing $15,000 to lure teachers into hard-to-fill positions with one-time financial bonuses.

Deck also said jobs will be juggled to cut out jobs in federal programs that have been axed and add personnel in areas such as art and music programs in elementary schools. Deck said he also has eliminated 25 administrative positions in the budget. He said those and other jobs have been left vacant by employes who have left their jobs.