After a long absence, the Presidential yacht Sequoia once again cruised the Potomac River last night -- and aboard were Mayor Marion Barry and some 25 local business and political leaders whose support is being sought by prospective candidates in next year's mayoral election.

The 21/2-hour cruise was organized by the Presidential Yacht Trust, a nonprofit group that purchased the Sequoia, sailed the craft from Florida to a permanent berth here and now hopes to make the boat available to President Reagan and to other public figures for social events. Last night's trip from East Potomac Park to the Wilson Bridge and back was "an introduction to Washington," said Michael Doud Gill, D.C. Republican National Committeeman and a member of the trust.

But Barry was the guest of honor. And his guests, in turn, included the kinds of local leaders that probable candidates have been pursuing for months.

"I'm not running for anything -- yet," Barry told the group in the stately wood-paneled main cabin of the 104-foot Sequoia as the yachting drew to a close.

But earlier, Barry's chief political aide, Ivanhoe Donaldson, had huddled with Washington Teachers Union president William H. Simons in an attempt to smooth over animosity between Barry and Simons stemming from an election last year for chairmanship of the D.C. Democratic party. Simons ran and lost and had believed he would get Barry's support for the post but did not.

And such guests as developer Jeffrey Cohen, the godfather of Barry's son Marion Christopher, speculated over the possible political combinations that could develop in the mayoral campaign: Will City Council member Betty Ann Kane run? Will council member John Ray? What about former council chairman Sterling Tucker?

Stewards hovered nearby with drinks and hors d'oeuvres and guests had a chance to tour the sumptuous yacht, which served eight presidents over a 56-year span. "I like to think this could really be a way of life," concluded Barry's wife, Effi.

Other guests invited by the mayor included realtor Flaxie Pinkett and civic activist Vi Curtis Hinton, both of whom have important ties to the city's middle-class black community, among whose voters Barry has never done well.

Also included were attorneys James Hudson and Vincent Cohen, and judicial nominating commission member William A. Borders. As the yacht cruised beneath lowering steelblue skies, the lawyers spent a good deal of time jocularly arguing with the real estate figures over whose profession was more "profit intensive."

At the end of the cruise after darkness had fallen on the river, Barry, who wore a white yachting cap, honored a tradition of the historic vessel by offering a toast to the president.

As the mayor raised a plastic cup to President Reagan, many of the Democrats on board appeared to show little inclination to follow his example, but he was enthusiastically joined by his Republican shipmates.