Del. Walter E. Fauntroy said yesterday he will seek reelection as the city's representative to Congress attempting to continue his reign as the only person ever to hold that 11-year-old job.

Fauntroy, who turned 49 Feb. 6 and who held a prayer breakfast yesterday morning to celebrate his birthday and the "Continuity of Building Together," said he would publicly announce his campaign for reelection at a fashion show and dance at the Washington Hilton Hotel last night featuring Count Basie.

"I sometimes feel discouraged," Fauntroy, a Baptist minister told the crowd of about 800 people at the prayer breakfast, "and I sometimes feel my work is in vain. I get discouraged when I see the nation blame its problems on the least among us . . . But the Holy Spirit revives my soul again. I feel good and I'm ready to keep on working for the Lord."

In an interview later, Fauntroy said he was anxious to run even though he apparently will face only his second challenger in a Democratic primary since he defeated Rev. Channing E. Phillips, Joseph P. Yeldell and others in 1971.

Marie Dias Bembery, a former assistant to Mayor Barry, has said she intends to run for Fauntroy's seat. She criticizes Fauntroy as an ineffective legislator who has not been able to get the D.C. Voting Rights Amendment approved.

"My record speaks for itself," Fauntroy said yesterday in answer to that criticism. "If we are not effective legislators we would not have gotten the home rule charter in 1973. We would not have gotten the Congress, by a two-thirds vote, to support the D.C. Voting Rights Amendment."

Fauntroy, who is the current chairman of the Congressional Black Caucus, has for years been considered one of the most popular politicians in the city. But lately, his power and the strength of his political organization have been drawn into question, and some city politicians attribute the absence of competition for his delegate's job to that job's non-voting status rather than fear of challenging Fauntroy.

He supported Clifford Alexander in the city's first mayoral election, former City Council chairman Sterling Tucker in the 1978 mayoral race, and Johnny Barnes, a former legislative aide to Fauntroy, in the 1980 City Council race in Ward 7. All three lost.