Maybe if they borrowed a competitor's jingle, they could sing: "Summit Special In The Air."

Reacting to a summit agreement providing for friendlier skies, United Airlines yesterday asked the U.S. Department of Transportation for authority to fly nonstop daily service between Washington Dulles International Airport and Moscow.

The request comes in response to an agreement reached last week between President George Bush and Soviet President Mikhail Gorbachev to expand air service between their two countries with the ultimate goal of doubling the capacity of passenger and cargo flights.

If its request is approved, United would begin daily nonstop service in April 1992 from its hubs in Chicago and Washington to both Moscow and Berlin. At least two other airlines also are seeking U.S.-Moscow flights in the wake of the agreement.

Although Pan American World Airways has authority to provide direct service from Dulles to Moscow, it currently provides only connecting service through Frankfurt, according to Vincent Rivellese, vice president for air service development for the Washington Airports Task Force.

Aeroflot, the Soviet airline, provides service between Dulles and Moscow with only a fueling stop in Gander, New Foundland.

No carrier provides direct service from Dulles to Berlin currently, he said.

The agreement between the United States and the Soviet Union provides for two U.S. passenger carriers to fly between Chicago and Moscow and for two passenger carriers and one all-cargo carrier to receive authority to fly between the Washington area and Moscow.

The fare for a round-trip flight between Washington and Moscow now runs just over $1,000.