The Arlington County Board yesterday unanimously approved a request by MCI Telecommunications Corp. to erect a large lighted rooftop sign on each of its two buildings in Pentagon City.

MCI officials had originally asked for permission to place up to 12 such signs, each 8 by 22 feet in size, on top of the two buildings, a request that was bitterly opposed by the National Capital Planning Commission. The federal planning agency complained that the signs would be visible from Arlington Cemetery, the Mall and the George Washington Parkway.

Two weeks ago, MCI amended its request to include only three penthouse signs, but the Arlington board delayed action until yesterday.

The planning commission, which has clashed with the county before over its approval of high-rise construction and signs visible from Washington, urged that, if there were going to be any signs, there should be only one on each building and they should face northeast--a compromise MCI agreed to yesterday.

Although the NCPC also wanted the signs to be smaller and placed below the 12-story rooftop, commission chairman Glen T. Urquhart said yesterday in a telephone interview "With the signs facing northeast, it's away from Arlington Cemetery and that was our first concern.

"The limited number and the fact the advertisement isn't facing Arlington Cemetery would seem to be an improvement from what it was originally.

Board vice chairman John G. Milliken, who moved approval of the signs yesterday, said, "This strikes me as a reasonable compromise . . . Businesses have some need for identifying where they are and putting themselves forth in a business-image way . . . (and) this protects the residential area around there."

Chairman Ellen M. Bozman agreed, saying, "I'm exceedingly pleased that MCI revised (the plans) because, on the question of putting signs high up on buildings, I think NCPC is right on target when it says it is unnecessary for signs to be obtrusive on a national monument."