The District Columbia will send a pro-Kennedy delegation to the Democratic National Convention in August, but its leadership will be divided between Mayor Marion Barry, a supporter of President Carter, and Del. Walter Fauntroy, a Kennedy supporter.

Local Democratic Party officials say when the selection process is finally completed, 11 of the District's 19 delegates to the New York convention will be pledged to Sen. Edward M. Kennedy, while eight are pledged to Carter.

Thirteen delegates were elected in the May 6 primary election. They then met last Wednesday to pick two more delegates -- one each for Kennedy and Carter -- and two alternates.

Barry was easily elected to fill the Carter slot, despite the fact that the Kennedy forces outnumbered Carterites 8 to 5 among the elected delegates.

Council member John L. RAY (D-At Large) was named Wednesday to the vacant Kennedy slot and Marilyn T. Brown, an active Kennedy worker, was chosen as an alternate. a

Wednesday's vote leaves four delegate slots still open -- two each for Kennedy and Carter. These will be filled by the Democratic State Committee on June 12.

Kennedy delegates elected in the May 6 primary are: Fauntroy, Kane, Council members David Clarke (D-Ward 1) and Nadine Winter (D-Ward 6), party workers Stephen Brown and Lillian Huff, realtor Flaxie Pinkett and teachers union president William Simons.

Elected Carter delegates are: Council members Wilhelmena Rolark (D-Ward 8) and Charlene Drew Jarvis (D-Ward 4), school board members R. Calvin Lockridge and Barbara Lett Simmons, and businessman John Hechinger.