Charging that Fairfax County and the rest of Northern Virginia have been shortchanged in gasoline supplies, the county Board of Supervisors yesterday voted to ask Virginia Attorney General J. Marshall Coleman to sue the federal government for more fuel.

The supervisors threatened to file their own suit if Coleman refused to do so and warned they may also sue Virginia to receive a larger share of the gasoline the state has been allocating during the shortage.

Northern Virginia has been the hardest-hit area of the state during the gasoline crunch. Several Fairfax supervisors said yesterday that state government has done little to help.

"We want to send a clear message to the state that we expect them to take action, and if they don't, we will," said Board Chairman John F. Herrity (R).

After meeting in closed session yesterday morning to discuss alternatives, the supervisors unanimously passed a five-part resolution including:

A request that Coleman file suit against the federal Department of Energy, similar to action taken last week by the Maryland attorney general's office. The supervisors said that federal allocations, which are based on last year's gas consumption, do not take into account the increase of cars and motorists in Northern Virginia since then.

A request for a meeting "as soon as possible" with Gov. John N. Dalton to discuss the state's "setaside" system, which the supervisors said also has shortchanged the area.

A plan to poll other localities to determine if they would join in suing DOE of Virginia.

A call for a meeting of the metropolitian area's Council of Governments to discuss gasoline prices here, which the supervisors said are a nickel or more a gallon above prices elsewhere in the country.

Coleman's office was unavailable for comment yesterday evening. Dalton's press secretary Paul Edwards said Coleman had consulted the governor about the possibility of filing suit against DOE but has not reached a decision.

Edwards said the governor was willing to meet with the supervisors or other local governing boards as soon as possible. He said Dalton had specifically ordered the state's energy office "to do everything it can to help Northern Virginia through the setaside program."

State Energy Office Director George Jones told a meeting of officials last Friday in Fairfax that the state had shipped 20 percent of its June setaside allocation to Northern Virginia and plans to do the same in July. But Jones said the area would not receive "preferential treatment."