Marie Bembery, a former special assistant to Mayor Marion Barry, began her campaign yesterday to unseat Walter Fauntroy as the District's nonvoting delegate to Congress.

Bembery said at a news conference on Capitol Hill that Fauntroy has failed to lead the effort for ratification of the constitutional amendment giving the District voting rights in Congress. She also said Fauntroy, who has represented the city in Congress since the office was created in 1971, has been ineffective in defending the District's Home Rule charter that gives the city limited self-government under Congress.

"There is no such thing as a do-nothing office, only do-nothing people," said Bembery, 39, who was known by her married name, Marie Dias, when she worked for Barry as a liaison to several groups of constituents.

She was fired by Barry last year after she told friends that she was considering a challenge to Fauntroy.

A resident of the Washington area since 1979, Bembery lived in the Maryland suburbs while working as a White House fellow during Gerald Ford's administration. She moved into the District to work for Barry.

Yesterday she said she has raised $46,120 of the $250,000 she believes she needs to challenge Fauntroy, who began his campaign in March.

She was endorsed yesterday by longtime Democratic activist Joseph L. Rauh Jr., who gave her a $200 contribution. Rauh, a proponent of the voting rights amendment, said Bembery has worked harder for the issue than Fauntroy.

"Maybe more importantly," Rauh said, "I want to protest Walter Faunt- roy putting his arms around PLO leader Yassir Arafat and singing, 'We Shall Overcome.' "

Fauntroy stirred criticism in 1979 when he and several other black officials attempted to intercede in the Middle East crisis, arguing that Israel should negotiate with the PLO.

Bembery said yesterday she will not take a position on the PLO issue, arguing that the District delegate ought to "take care of problems here first."