The Fairfax County School Board called last night for a sharp increase in school spending, setting the stage for a confrontation with the conservative-minded county supervisors, who provide most of the money.

The $345 million budget request that the school board approved last night is up 20 percent over current spending, with much of the increase earmarked for teacher raises and escalating energy costs.

County officials say that the spending increase could force the real estate tax rate up and add about $187 to the tax bill of the owner of the average home.

The budget would require $217 million of county funds -- $34 million more than the county's present contribution.

School board members say they expect the county board of supervisors to make some cuts in what School Board Chairman Rodney F. Page has called a "catch-up" budget.

One goal of the budget is to improve teacher morale by providing 8.5 perent raises for all school employes. Teachers initiated a "work-to-the-rule" job action last year, partly because they were dissatisfied with their pay.

School board members said the budget request is so large because of two factors: Gov. John N. Dalton's austere state budget proposals and rising energy costs.

Dalton's education budget has been attacked as unfair by school board members, who indicated they would explore the possibility of going to court to force him to increase funding for public education.

School administrators increased their estimates of next year's energy costs by $3 million during the past month, bringing that figure to $19 million. cThe uncertainty over the price of energy is underscored by a note in the budget that reads: "It is the staff's view that the energy crisis has the potential for gross disruption of the instructional program in F.Y. 1981 and beyond."

Energy conservation has been a bone of contention between the school and county boards since last spring when the educators voted to increase walking distances for students as an energy and budget-cutting measure. The supervisors countered by allocating more funds to the schools to keep buses on the roads.

Supervisor Joseph Alexander, (D-Lee) said yesterday he was concerned about the school budget.

"I'm not personally convinced they (school administrators) have done everything possible to conserve energy," Alexander said. "I'm going to propose that the effectiveness of the area offices be examined as a way to cut the budget. This is not my idea, it's coming from people within the system who question the need for all those layers of bureaucracy."

Alexander added that it is his opinion the supervisors "certainly don't want to increase taxes this year."

School Board Vice Chairman Ruth H. Dell yesterday called the budget "unique for two reasons. One because of the uncertainty on the review side -- from both the state and federal levels. Two, there is the big threat in terms of energy costs."

"The only way to look at this budget is as a fair statement of the needs of the school system," she continued. "It would be foolish for us to say we expect the county to make up funds being reduced by the state."