D.C. Democrats took their first formal step yesterday in the 1988 presidential campaign, nominating candidates to run for posts as national convention delegates in the city's May 3 presidential primary.

More than 1,000 registered Democrats turned out for the daylong caucus at the Washington Convention Center, which drew organized efforts by the campaigns of several presidential candidates.

As expected, supporters of Jesse L. Jackson turned out the most participants -- more than 500 -- with the campaigns of Sen. Paul Simon (D-Ill.) and Massachusetts Gov. Michael S. Dukakis vying for distant second-place finishes.

There were smaller turnouts for former Arizona governor Bruce Babbitt, Rep. Richard A. Gephardt (D-Mo.), Sen. Albert Gore Jr. (D-Tenn.) and former senator Gary Hart of Colorado. At least one person showed up to promote the campaign to draft New York Gov. Mario Cuomo.

The caucus yesterday was the first step of a complex process in which District Democrats will select 24 delegates to attend the Democratic National Convention in Atlanta in July. Under party rules, the 24 delegates must be equally divided between men and women.

Of the 24 delegates, 13 delegate slots will go to party officials and elected leaders who will be chosen at a meeting of the D.C. Democratic State Committee on June 9. The remaining 11 delegates -- the focus of yesterday's caucus -- will be chosen in the city's May 3 Democratic presidential primary.

Under caucus rules, supporters of each presidential candidate met in separate rooms at the convention center yesterday. Each political camp then nominated candidates for delegates. To qualify for slots on the May 3 ballot, those candidates must collect 1,000 signatures of registered Democratic voters by March 4.

Rather than having all 11 delegates elected citywide, the Democratic Party treats the District as a state and divides the city into two congressional voting districts.

Congressional District 1 is made up of Wards 1, 2, 6 and 8. Democratic voters in those wards will choose five of the 11 delegates in the primary. Congressional District 2 is made up of Wards 3, 4, 5 and 7 and Democratic voters in those wards will elect six of the 11 delegates.

Mayor Marion Barry, who is supporting Jackson, was among many prominent Democrats who showed up for the caucuses yesterday. Barry was not a candidate yesterday because he likely will go to the national convention as one of the 13 delegates chosen by the party in June.

Top vote-getters at yesterday's caucus included several elected city officials who also are supporting Jackson. Among them were Del. Walter E. Fauntroy (D-D.C.), Council Chairman David A. Clarke and council members Nadine P. Winter (Ward 6), H.R. Crawford (Ward 7) and Frank Smith (Ward 1). Among those who are not elected officials, Bernard Demczuk, a national organizer for the American Federation of Government Employees, appeared to be leading most balloting for a Jackson delegate slot.

The Dukakis campaign nominated three council members to represent the Massachusetts governor -- Jim Nathanson (Ward 3), Charlene Drew Jarvis (Ward 4) and Betty Ann Kane (At Large).

The Simon campaign also claimed several well-known city political leaders, including school board members Bob Boyd (Ward 6) and R. Calvin Lockridge (Ward 8).

Political leaders in the city have generally said that Jackson, who easily won the city's primary in 1984, likely will repeat that showing and that Simon and Dukakis will fight for second place.