There was no bursting into song, which he's been known to do at parties, but Zambian President Kenneth Kaunda showed off one of his other talents last night: how he can draw a crowd.

The more than 500 high-level administration and diplomatic guests who jammed into a Four Seasons Hotel ballroom to meet the 59-year-old African leader were so eager to shake his hand that they went through a receiving line twice.

The first time was before Kaunda arrived, when Zambian Ambassador Putteho Ngonda and counselor Sylvester Kabati, with their wives, welcomed everybody. Going through that line was Soviet Ambassador Anatoliy Dobrynin, celebrating 21 years to the day that he presented his credentials to President John F. Kennedy.

When a guest asked if he would be leaving Washington, Dobrynin grinned broadly. "Certainly," he said, "but when, I don't know--I don't have any information. Of course, I read about all the promotions I get in the American press."

The second receiving line go-round got under way when Kaunda and his wife, Betty, arrived shortly before 7 p.m. By that time, however, Dobrynin had gone off to another engagement.

Secretary of State George P. Shultz's arrival gave an extra dose of symbolic clout but no extra news about Kaunda's two-hour talk with President Reagan earlier in the day. "I don't give interviews at parties," said Shultz.

Somewhat more loquacious was U.S. Ambassador to Zambia Nicholas Platt.

"The important thing to remember is that the United States and Zambia have the same objectives. Everybody wants to see neighboring Namibia free, peace in that region, stability and economic development. President Kaunda is here to figure out the best way to do that. His views are very much respected."

Almost every African chief of mission to Washington was in the crowd that roamed between buffet tables laden with platters of giant shrimp, lobster, oysters Rockefeller, crab claws, steak tartare, smoked salmon and assorted canapes and cheeses. A spread that one source estimated to cost the Zambian government about $25,000, it succeeded in making Zambia's economic problems seem remote, although Kaunda's schedule today includes sessions with officials at the Agency for International Development and the World Bank.

"What African countries need is more economic development--in agriculture, not military," said Ohene Darko, president of the Continental Africa Chamber of Commerce. "African countries try to minimize equipment and conflict."

Of concern to the Africans was what Kaunda has described as an "unnecessary deadlock" with the Reagan administration over Namibian independence and withdrawal of Cuban troops in Angola.

"There is a little bit of a vicious circle," said Portuguese Ambassador Leonardo Mathias. "The Zambians are siding with the Angolans, who say, 'The Cubans will withdraw once we are not threatened by South Africa.' The Americans have a different view. But Kaunda is a very moderate man, highly respected in Africa, so I think it was useful for him to come and for Reagan to listen.

"Diplomacy is always a phenomena of interaction," Mathias continued. "That's what diplomacy should stand for."