"Every performance ran late," Konstantin Zaklinski of the Kirov Ballet reminisced last night. "The fans in Los Angeles did not want to let us go."

Zaklinski, who dances the lead in tonight's performance of "Swan Lake" at Wolf Trap, was at a preopening reception that did not run late, yesterday at the Soviet Embassy. Although this is his first visit, he said he does not feel like a stranger in the United States. "I know a lot about America. I have seen a lot of American movies on video."

The parts of America he was able to see at the embassy last night included Secretary of State George Shultz, Director Charles Wick of the U.S. Information Agency, Beverly Sills, who is a board member of Wolf Trap, and a guest list of distinguished Washington arts enthusiasts. The Kirov Ballet's reception in the United States has been "very warm," prima ballet mistress Olga Kolpakova said. She was referring to American audiences' "very emotional" reaction to the Leningrad company's performances, but her colleagues in the corps have found other kinds of warmth.

"We got sunburned in California," Ljuba Kunakova said. "It was wonderful." But all of the ballerinas at the party found the Washington climate "very hot." Kolpakova, who has visited the United States before, says that San Francisco is her favorite American city, perhaps because it is "on the sea," like Leningrad.

Within a day of their arrival, the dancers had not yet seen much of Washington, but they noted with approval the "lack of skyscrapers" and the abundance of parks and greenery. They have seen the Washington Monument and enjoyed the Mall.

"When you dance a lot, you get tired, and it's hard to see the sights," Zaklinski said. "You can't go out in the evening if there's a performance." In Los Angeles (where he did manage to see a place that sounds like "Gollyvood" in Russian), he was impressed by "the variety of nationalities" in the United States.

The reception was given in the Gold Room on the second floor of the embassy on 16th Street NW -- a room that would have been called the "Imperial Ballroom" in the embassy of a less proletarian power. Its high ceilings, gold-inlaid Ionic columns and hardwood floors evoke the elegance of an earlier age -- and, in fact, it was built when the embassy on 16th Street represented the czarist government. Today, an enormous oil portrait of Lenin looks quizzically at the room's opulence from an adjoining foyer.

Six buffet tables were spread across the room, laden with smoked salmon (which disappeared first), caviar, cold meats, jellied ham and fish. Fruits (in watermelons hollowed out into basket shapes) were the centerpiece of each table.

The caviar was spread on little biscuits speared with toothpicks. "I expected to see bowls of it," said one disgruntled guest. The bars at each end of the room served Georgian wine and Russian champagne, soft drinks and fruit juices. "No vodka?" asked one guest. The bartender (whose English vocabulary seemed limited to "Ice?") shook his head, a bit sadly.

Catherine Filene Shouse, host of the Kirov Ballet at Wolf Trap, presided over the meeting in a wheelchair, wearing the satisfied smile of someone who has sold all the tickets for her current attraction. She began the evening by exchanging diplomatic courtesies with Oleg Sokolov, the Soviet charge' d'affaires: "We're so pleased to be opening with the Kirov." "Yes, it's a wonderful company. They were last here -- what is it? -- 22 years ago."

Oleg Vinogradov, the artistic director of the 200-plus-year-old company, is largely responsible for its distinctive character today. He likes to discuss it.

"You do more contemporary ballet. We build on a long classical tradition, with ballets based on literary works. We consider it important to pass this tradition on."

Despite this traditional orientation, he promised "a surprise -- more contemporary" somewhere in the run at Wolf Trap.

One of the dancers (not speaking for attribution) said there would be three contemporary works, probably in the last performance Thursday night.

There were no surprises from the Reagan administration figures at the reception, all of whom seemed, for the occasion, wildly enthusiastic about cultural exchange. In a conversation with the assembled dancers, simultaneously translated by Sokolov, Shultz said that "music and dance are an international language and a way of affecting each other through the best of our cultures." Asked whether he saw the Kirov's visit as a sign of hope for better Russian-American relations, he half-avoided the question: "They said they were very warmly received wherever they went."

Wick said that cultural exchange is "a process that just has to be."

On the value of cultural exchanges, he said, "I never saw a performing artist or a great painter start a war."

But cultural exchange involves "complex logistics," he said. "We at USIA want to be catalysts for the private sector."

"There is a lot going on below the star level," according to Stephen Rhinesmith, coordinator of the president's U.S.-Soviet Exchange Initiative, which did not originate but helped to coordinate the Kirov's U.S. tour and Vladimir Horowitz's visit to the Soviet Union. Cultural exchanges still in the discussion stage range through many levels, he said, including amateur choral groups, high school basketball teams, medical personnel in such fields as alcoholism and drug abuse as well as a "Sister Cities" program to link American and Soviet cities.

The next Soviet group visiting America will be a jazz trio that is planning a two-month tour. On the star level, the Moiseyev Ballet and the Moscow State Symphony will be coming in the fall, and the Bolshoi Ballet next year.

What does it mean to American audiences? "I've been going to the ballet all my life," said one fan at a buffet table, "and I love 'Swan Lake' and I've never seen it done complete. We don't do it that way in America. I'm hoping that the Kirov performance will be complete."

And what do American audiences mean to the Russian dancers? "We have been getting such phenomenal receptions, it makes the dancers dance better," Vinogradov said.