Fairfax County Commonwealth's Attorney Robert F. Horan filed an unprecedented lawsuit yesterday against the Board of Supervisors to force the county to lower next year's property tax rate.

Horan, the elected county prosecutor, said the suit could affect budgeting decisions in jurisdictions throughout Virginia. The case could also prove embarrassing for the county's nine supervisors, who say they have been bombarded with calls and letters protesting rising home assessments.

The Fairfax County Taxpayers Alliance, whose several thousand members regularly oppose tax increases and bond issues, had petitioned Horan to sue on the grounds that the board set aside too large a reserve fund when it adopted the fiscal 1983 budget last month. The taxpayers group contended the supervisors set aside more than $20 million so they would not have to raise taxes next year--when they must stand for reelection.

The county has 21 days to respond to the suit, which asks a Circuit Court judge to order the supervisors to lower the tax rate by an unspecified amount. County officials said yesterday their adopted budget is prudent and proper.

Under a Virginia law that has never been invoked in Northern Virginia before, Horan was required to file suit by yesterday after more than 1 percent of the county's 278,000 voters petitioned him to do so. Elections officials certified yesterday that enough of the 4,000 petition signatures are valid to satisfy the law.

Horan said, however, that he is not reluctant to follow the law and that he believes the taxpayers petition is not frivolous, as some county officials have claimed.

"I think they've got some legitimate claims," he said. "It's not the kind of thing to dismiss lightly just because it hasn't been tried before."

The suit is the second Horan has filed against the nine elected supervisors this year. In January he sued the board for holding a secret meeting in violation of the state's Freedom of Information law.

Horan, who yesterday opened his campaign for the Democratic Party's Senate nomination, was slower to respond to the citizens' request to pursue the Freedom of Information case, and some officials speculated he was reluctant to sue his allies on the board. Horan acknowledged that the taxpayer's group petition could cast him in the more favorable light of battling for balanced budgets, but he said that would not affect his prosecution.

"I'm sure it has political overtones, but I'm more interested in the legal realities," he said.

Horan said the state constitution allows governments to levy taxes for the "necessary expenses of government," a term that has never been defined in court. He said a judge might decide that large budget reserves for future years are unconstitutional.

County officials said their reserve is modest, given the $564 million budget, and necessary because of the recession and uncertainty over future federal budget cuts. In a statement released yesterday, the county said state law specifically allows a "reasonable reserve for contingencies."

The board lowered the tax rate from $1.51 to $1.47 per $100 of assessed property for 1983, but because of higher assessments the average home tax bill will jump by $102 to $1,453.