A few hours after emerging from his jet yesterday into the hot morning sun of this historic center of black African culture, District of Columbia Mayor Marion Barry said he had experienced a "spiritual awakening."

Though he looked tired after the long flight, and the official welcome he received was a modest one, Barry said he was "charged up" throughout the first hectic day of his two-week, five-nation African tour.

There has been generalized talk about eventual economic and cultural exchanges between the District and various African cities, especially Dakar, but Barry's first hours on the continent to which most Washingtonians trace their roots were devoted to more symbolic and emotional links.

As he met with various officials, including Dakar Mayor Lamine Diack, Barry wore a variety of pins and pendants silhouetting the African continent, changing from a gold to silver one when he changed from his beige safaru suit into a more formal seersucker for the afternoon and evening.

The members of Barry's party - his wife Effi, aide Courtland V. Cox, D.C. Democratic leader Robert B. Washington Jr. and Riggs National Bank Vice President Carter H. Dove - were also enthusiastic, though the day was not without its snags and initial misunderstandings.

The crowd at the airport was small, a reporter was told, because the U.S. International Communication Agency (ICA), which is paying for the trip, decided to make it low-key.

There are apparently fears that the inclusion of Dove in the party might spark protests because of his bank's reported involvement in financing some South African industries.

Some political groups in the United States concerned with African affairs have been making efforts to bar Dove from attendance with Barry at an Organization of African Unity meeting in Monrovia, Liberia, later on the trip.

But Barry said that only he, his wife and Cox had been invited to the OAU session, so Dove would not be going anyway.

Barry's party was also pointedly informed that Mayor Diack and members of Dakars City Council would be dressed in business suits at their meetings with the Washingtonians and the Americans' safari-type attire was altogether too informal, but dark suits were not part of the wardrobe brought by most members of Barry's party.

"There is a spiritiual bond between mayors, although we may not speak the same language," Barry told Diack at the city hall meeting.

Barry seemed intrigued with parallels between Dakar and the District of Columbia as federally controlled capitals, and there was continuing talk of their becoming "sister cities."

Among the ideas Barry said he has gleaned from discussions here are a "peace corps" for the District to aid residents of public housing projects, as well as "technical and cultural exchanges."

Barry told a television reporter that "one of the first purposes" of the visit is "personal pleasure," and he said later that "even if the citizens of the District don't get a thing out of this, it would still be worth it to get a different perspective."

It is the culture of Senegal, of which officials in this center of African intellectualism are justly proud, that most impressed the mayor and his party. While an American bank director in Dakar who met with Barry said he was a bit puzzled by the purposes of the mayor's visit, a great deal of excitement was generated among the Senegalese by the prospect of sending a major exhibit of their art to the U.S. capital.

This is one of the projects that Barry said he hoped to discuss with Senegalese President Leopold Senghor - a poet with an international literary reputation as well as a politician - when they meet Sunday evening.

It was a long first day in Africa, but one the visitors seemed reluctant to end. When the official functions were over, they danced until well past midnight to the strains of American disco music.