They stood. They smiled. They went into a hand-shaking clinch. Tooth to tooth, grin to grab, gray pinstripe to blue pinstripe: Don King meeting Marion Barry.

It happened just after high noon yesterday, when boxing promoter King with his 120-volt hair and two-story diamond ring unfolded his bulk from a long black limo and walked up the steps into the District Building for a talk with Mayor Barry. He tripped the metal detector as he went through the door, but you could hardly hear the shrill beeeeep for all the Good-Afternoon-Mr.-Kings emitted by the security guards.

And after all, who was going to mess with the guy who promoted the "Thrilla in Manila" (the Muhammad Ali-Joe Frazier fight in the Philippines in 1975) and the "Rumble in the Jungle" (The Ali-George Foreman bout in Zaire in 1974), a man who has been known to wear a floor-length, fur trimmed purple cape and shirts with lavender ruffles, opened, of course, to reveal gold chains the likes of which could be used for boxing ring ropes? The man, even in slender pinstripes, is a building on a hike.

King was in the nation's capital yesterday to talk to the mayor about boxing capital, the kind it would take, King said, to "revitalize boxing in Washington, D.C., and to bring some major, world quality events."

It was the second meeting for the numbers runner-turned-boxing promoter and the civil rights activist-turned-mayor. The two first met last month when Barry, mostly at the expense of the D.C. Armory Board, went to Las Vegas to watch Sugar Ray Leonard whip Thomas (Hit Man) Hearns, and to explore "new and different ways to create economic development in Washington," Barry said yesterday.

For his part, King said he offered Barry the possibility of bringing several bouts to the District, including a fight between welterweights Roberto Duran and Wilfred Benitez. No specifics have yet been discussed, King said.

"Since I do not suffer from any lack of money, I want to reciprocate," said King, as he majestically waved his right arm toward a television camera.

"There are a lot of things we can do here," King said, "as long as I'm agreeable."