The Justice Department has filed suit in federal court in Alexandria to block Fairfax County from forcing the 1,500 children who live at Fort Belvoir to pay for their education in county schools.

The lawsuit against Virginia and the Fairfax School Board is the first in the nation aimed at thwarting local attempts to penalize military families for the expected loss of millions of dollars in federal impact aid.

The House of Representatives has agreed to a cutback of about 37 percent in those funds, which the federal government traditionally has granted areas like Northern Virginia to compensate for nontaxable federal installations there.

Virginia Democrats seized on the suit yesterday as evidence that Republican state Attorney General J. Marshall Coleman does not have the influence with the Reagan administration that he has claimed during his current campaign for governor.

Ben Ragsdale, a spokesman for Coleman, said Coleman tried to negotiate the dispute and avert a lawsuit. Ragsdale also said Coleman stood by the constitutionality of a new state law that grants localities the authority to charge the tuition.

"We have said emphatically that the county has the right to do that," Ragsdale said. "We think we have a constitutional law there."

Fairfax officials this fall notified the parents of more than 1,500 children at Fort Belvoir that they would have to pay for part of their children's public education if Congress implements the cuts President Reagan wants.

The Defense Department has claimed the charges would unconstitutionally discriminate against children whose parents happen to serve in the military. The suit, filed late Friday, names 11 Belvoir parents as plaintiffs and claims the new Virginia law is superseded by federal laws prohibiting taxation of military families in more than one state.

Threatened with the loss of $6.9 million in federal impact aid, the Fairfax school board is the only one in the nation to threaten military families with tuition charges.

Fairfax officials declined to comment on the suit. They have previously said that because most families living at Fort Belvoir do not pay county property tax or state income tax -- the two chief sources of funds for public education -- the federal government should contribute to the costs of running the three county schools on the base.

"Somebody has got to come forward and rescue them the children ," school board Chairwoman Ann P. Kahn said when the board voted to charge at least $2,600 per student in September. "But it is not incumbent on the taxpayers of Fairfax County to pay the $4.4 million cost of educating these children."

The Senate is expected to consider the House cuts in the impact aid program during the next two weeks.