The first segment of Metro's Green Line, the subway system's only unopened branch, will begin operating May 4 in the District, General Manager Carmen E. Turner said yesterday.

With three new stops, passengers will be able to travel 1.6 miles between the Gallery Place-Chinatown and U Street-Cardozo stations in Northwest Washington.

Heading north from Gallery Place, the stations are Mount Vernon Square-UDC at Seventh and M Street, Shaw-Howard University on Seventh between S and R streets, and U Street-Cardozo on U between 10th and 13th streets.

The stations, which are along a segment of the Green Line that will be completed to Greenbelt in Prince George's County by 1993, will add about 5,700 weekday passengers to the subway system, many of them poor and dependent on mass transit.

Originally scheduled to begin service Dec. 1, the stations' opening date was pushed back five months because of a bitter dispute between Metro and the contractor, who was fired in May and replaced.

The new contractor, Perini Corp., has been working furiously with 245 workers to correct problems, which left pavement torn up in the Seventh Street and 14th Street corridors. Residents and businesses have complained about the conditions for months.

Most of the underground work has been finished and trains have been tested. The biggest remaining obstacle is access to the stations from the streets.

Metro also has set a date for the 1991 opening of the station at Van Dorn Street in Alexandria, but will not disclose it until board member Joseph Alexander of Fairfax recovers from surgery he had yesterday.