The Army Corps of Engineers, which has been bitterly attacked by some Fairfax County officials for the power it holds over the metropolitan area's water supply, has offered to supply the county's future water needs for a third of a century.

If the Fairfax County Water Authority accepts the offer, the corps would become an even more powerful force regionally. Already it supplies the District, Arlington, Falls Church and even part of Fairfax, and decides which localities can tap the Potomac River for water.

The corps, sensitive to the criticism it has received in Fairfax, hasn't been shopping around for new customers. But the Fairfax County Board of Supervisors, with some members swallowing their hard feelings about the corps, had asked the authority to seek a water supply proposal from the corps.

The supervisors are on record supporting the water authority's plan to take care of its future needs all by itself - by tapping the Potomac River. At present, the authority, which supplies Alexandria and part of Prince William county as well as Fairfax, must rely on its Occoquan Reservior - a source that will be inadequate by 1981.

But the authority is encountering new difficulties in its long-standing attempt to get a Potomac River permit from the corps. The latest objection comes from the Interior Department's Fish and Wildlife Service, which doesn't want the corps to give a permit until there is a study on how much water should remain in the river in order to maintain its current ecological diversity.

The corps said in a recent letter that Washington's-Dalecarlia plant - which the corps operates for the city - is good enough to supply the Fairfax authority's needs to 1990 and could meet demand to the year 2010 with additional pumps.

The corps' acting district engineer. Lt. Col. John H. Kenworthy, said: "If (the secretary of the Army) agrees to the sale, and the necessary concurrence is obtained from the District of Columbia, I believe the parties involved could resolve most, if not all of the (authority's) concerns . . ."

The water authority's assistant director, Fred P. Griffith Jr., said the corps' proposal "was a probability, and it probably should be looked at." He added, however, that no decision could be made before an analysis was done on the costs of buying the water and piping it to Northern Virginia.

The authority's original plan to build its own Potomac facility means the authority won't be using the new supply until 1981. But even that date depends on issuance of a permit from the corps by July and no construction delays, the water authority has said.

Officials familiar with the corps' permit process said the agency is unlikely to grant the permit until the new objection from the Fish and Wildlife Service is resolved.