Alexandria City Councilman Nelson Greene, the only black on the seven-member council, has announced that he will not seek reelection in the city's May 4 elections.

Greene, a 65-year-old undertaker and a Democrat, said he was frustrated by his inability to press the city government toward meeting the requests of Alexandria's black community. Although Greene had said when he was elected in 1979 that he would seek only one term, Democrat leaders tried this year to persuade him to change his position.

"Disappointment is an understatement," said Councilman James Moran, a Democrat. "I can't imagine any way someone's arm could have been twisted more ways than Nelson's was on this thing."

Although bowing out of office, Greene has endorsed Lionel Hope, an auditor at the University of the District of Columbia, as a possible successor. Hope, who long has been active in Alexandria civic affairs, was Greene's campaign treasurer in 1979.

Greene said he hoped that if Hope wins he would not be viewed only as a mouthpiece for blacks -- a role that Greene said befell him as the only black councilman. "I don't want Lionel to end up like I ended up," said Greene. "I'd like to see two or three blacks on the City Council."

Greene cited a 1979 controversy over the Confederate statue that stands in the middle of Washington Street as typical of his frustrations. Greene opposed spending city money to refurbish the statue and requested that it be removed from the city's main thoroughfare as offensive to blacks.

"I told them the best place to put it was in the Potomac," Greene said. The council voted against allocating city money to restore the statue, but did not order it removed.

Another disappointment Greene noted was a council vote earlier this year that decreased black representation on city school board from three to two at a time when the city's blacks make up majority of Alexandria's public school population. "The school board issue set me off," Greene said yesterday. "I couldn't understand how, if the city's not going backward, they could do that sort of thing. The only thing I can think is it's racist."