Fulfilling a campaign promise, Mayor Marion Barry met over breakfast with more than 100 members of the clergy yesterday and asked them to help his administration solve some of the city's most pressing social problems.

Meeting at the New Bethel Baptist Church, First Street and Rhode Island Avenue NW, Barry called on representatives of all denominations in the city to welcome young people not committed to any religion. He predicted many would become active in the congregations.

"Organize young people... ask what you can do... reach out," Barry urged his listeners.

By doing this, Barry said, churches may be able to help solve such social problems as teen-aged pregnancies and births out of wedlock. "Over 40 percent of all births in this town last year were to mothers under 19," he said, including 59 percent who were unmarried.

Barry also said churches could help identify elderly parishioners who are in need of food available under city sponsored programs but are too proud to ask for help.

During last year's campaign, in which he apparently drew the least support from religious leaders of any of the three major Democratic aspirants, Barry promised -- if elected -- to meet with the clergy and to maintain regular contact. He has appointed a special assistant, Matthew Shannon, as his religious liaison.

"I didn't vote for him," said the Rev. Leamon W. White, pastor of the church and president of the city's Baptist Convention. "But now that he is the mayor, we are trying our best to give him the support he needs for a better and more united city."