The Fairfax County Taxpayers Alliance, a conservative group that claims several thousand members, petitioned the county's prosecutor yesterday to sue the county supervisors in an effort to force lower real estate taxes.

The petition, which the alliance claims was signed by 3,798 people, alleges that the supervisors recently set aside too much money for a reserve fund when they should have lowered real estate taxes. Under Virginia law, Commonwealth's Attorney Robert F. Horan is obliged to sue the board upon receiving a petition signed by more than 1 percent of the county's registered voters, according to County Attorney David T. Stitt. There are about 278,000 voters in Fairfax.

County officials said yesterday they are confident their budget decisions, which have been protested regularly by the taxpayers' group, will be upheld in court. But the lawsuit, apparently unprecedented in Fairfax, could be embarrassing for the nine supervisors, already under attack because of rising tax assessments. It could be unsettling as well for Horan, who announced Sunday he will seek the Democratic Party's Senate nomination and who recently sued his allies on the board for holding a secret meeting in violation of the state's Freedom of Information law.

James W. Roncaglione, president of the Taxpayers Alliance, said state law permits the board to levy only enough taxes to cover legitimate expenses. This year, he said, the supervisors violated that provision by establishing a $27 million reserve, a fund Roncaglione said they created because they do not want to raise taxes next year when they face reelection.

The supervisors have said the contingency fund is reasonable and necessary because of the current recession and cuts in federal aid. Stitt, who would defend the board in court, called the legal action a "farce."

He also said Virginia law should be changed to give the prosecutor some discretion in responding to such a petition. "You could probably get 2,800 signatures to get Fairfax County to declare war on the Falklands," Stitt said.

Roncaglione said the signatures, collected in a 2 1/2-week period, reflect voter dissatisfaction with rising taxes. 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 tax bill will jump by $102 to $1,453.