More than 800 people showed up at a Libyan reception last night, and before the evening was over, many found themselves doing an Indian dance.

"We have come here to meet the American people," said Ahmed Shahati, head of the Libyan delegation that has been on a 10-state tour of the United States, sometimes ushered by Billy Carter. Last night, in the Dolley Madison room of the Madison Hotel, he met about twice as many as had been originally invited.

"Our original guest list was 400," said Claire Frances Stahl, social liaison for the Libyan delegation, "but then more people wanted to come and friends wanted to come and it just grew."

Most of the Americans met by the Libyan delegation last night seemed to be Americans they had met before. The list included executives of corporations doing business with the Libyan government, a large contingent of Arab-Americans, several out-of-office politicians and of course Billy Carter.

The most notable group of strangers were 24 American Indian dancers and some officers of the National Congress of American Indians, who had been invited perhaps because, as Shahati put it, "The Libyan people believe in freedom for all peoples of the world; we favor liberation movements everywere."

At the climax of the evening, the Indians did their "dance of intertribal and international friendship" and asked everyone to join in. The drums set up a steady two-beat rhythm, the dancers in their feathered headdresses and ceremonial robes joined hands and began to circle, stamping out the rhythm, and spectators slowly moved from the sidelines into the dance.

A few were in formal black tie or evening gowns. Most were in business suits, and many were in the native costumes of Libya: djellaba and fez (worn with a white shirt, no necktie) or the flowing robes of the desert people, with burnoose and a cloth covering all of the face except the eyes.

As the dance went on, Shahati joined it, holding hands, his long white robe swaying gracefully, his face beaming with obvious delight. A Libyan spokesman called it "a response from the original Americans to the authentic Arabs."

Carter appeared briefly early in the evening, was engulfed by reporters whose questions he fielded for a few minutes, and then disappeared to quieter surroundings for about an hour while the guests nibbled at a lavish buffet of Western and Middle Eastern hors d'oeuvres or dampened their spirits at the rather austere bar. "You can have anything you want," said a bartender, "as long as you want soft drinks, fruit juices, coffee or Perrier water. They don't believe in alcohol."

When he reappeared, Carter was asked to give a speech but spoke for less than a minute, pleading laryngitis.

"I'm not a speechmaker," he added, fumbling for something noncontroversial to say. Then his face brightened, he pointed to an infant being held by its mother in a corner, and his problem was solved: "That's a real pretty baby over there, I'll tell you that." End of speech.

Besides Carter, the American dignitaries getting the most attention were ex-senators J. William Fulbright, James Abourezk and Albert Gore. Early in the evening, Abourezk didn't seem quite sure why he had been invited, explaining simply that he had "met the Libyans through friends at other embassies." By speech-making time, however, he had found something to say. He called the Libyan delegation members "very capable, intelligent, civilized -- nothing like what you read in the popular press, armed to the teeth with hand grenades and running around trying to terrorize everyone.

"Despite what the lobby of the government of Israel tries to do," he said, "I predict that there will be better relations between Libya and the United States."