Twelve stories above the East River with a scarlet Pepsi Cola sign flashing from Queens. United Nations Ambassador Andrew Young looked at his audience. "No one of us would have thought in 1960," and he paused, his brow deeply creased, "or in 1965 or in 1970, or even in 1976 that this kind of gathering would have been possible."

The tone of mocking disbelief was intentional, and his audience of ambassadors to the United Nations and other diplomats, laughed immediately realizing the not-so-long-ago improbability that the guests of honor from Washington could dominate City Hall or stake out Cabinet posts.

He was introducing the new Washington leadership to the international community in New York last night. D.C. Mayor-elect Marion Barry, D.C. City Council Chairman-Elect Arrington Dixon, Secretary of Housing and Urban Development Patricia Roberts Harris and D.C. Delegate Walter Fauntroy were the guests of honor at a reception at the U.S. mission headquarters across from the United Nations. Some 75 ambassadors or other foreign representatives were among the guests.

It was "the warm faces, not the stone monuments" that Young and Washington businessman John Hechinger, currently a delegate to the U.N., wanted to show off last night. "We especially wanted to show the black government of Washington, the living city, the government you don't usually know in the diplomatic world," said Hechinger, who noted that more heads of missions had showed up at the party than any other party the American delegation to the United Nations has given this season.

This was the first time the U.N. mission had held a reception for any local officials. Could Washington's image as a city of statues and senatorial speeches be erased in one evening? Sen. Abraham Ribicoff (D-Conn.) was optimistic. "With Andrew Young's position and this show of black leadership, we should be able to gain extra confidence with the African countries," said Ribicoff.

But at times the two-hour reception had the stiffness of a teen-age social, with the Washingtonians and the diplomats drinking Shasta soft drinks, Wente Brothers chablis and nibbling curried chicken and quiche.

Even after the receiving line broke up. the pattern was to shake hands, exchange greetings and then retreat to someone familiar. "What I hope to push is more cultural exposure, both from the Washington community and the diplomatic community. That's a tremendous educational opportunity for our youngsters," said Dixon.

Many of the ambassadors and other U.N. delegates-and the Washington contingent-wanted a word with Young, who had just returned from an 11-country trip late yesterday afternoon. He had an audience in Rome with Pope John Paul II "and found his interest in Africa compelling. But he let me do all the talking."

Young reported to U.N. Secretary General Kurt Waldheim, "We have patched up the relationship with the Front Line states," referring to the five black African countries that are pivotal U.S. allies on the southern African questions. Young characterized the trip as one of mending fences with the black African states over their disapproval of Rhodesian Prime Minister Ian Smith's recent visit to the United States and the South African government's intention to hold its own elections in Namibia.

"Our African policy depends on honesty and communication. At times we do not have direct communication, so I went to personally offer our position," said Young. In addition he told Waldheim that the black African countries "still don't think Ian Smith is ready to talk" on the question of majority-rule elections in Rhodesia.

The reception was the first official opportunity for Mayor-elect Barry to test his prowess on the diplomatic circle. Barry, who arrived almost an hour after the party started, appeared relaxed with the endless congratulations thrust at him. He said the party was a testing ground for some of his ideas for activating the mayor's political participation in the international area. Previously, the Washington mayor has played only a ceremonial roll at state visits and national day parties in Washington.

"Frankly, I think we have ignored the international community, especially on an economic and social level," said Barry. In recent weeks, he has met with Secretary of State Cyrus Vance and protocol chief Kit Dobelle, he said, on controversial issues such as diplomatic parking previleges and the number of chanceries in residential neighborhoods. Also I think more of the embassy staffs should live in the city. Over all I want to take a more vocal role in international politics."

The diplomats seemed to accept the subtle fellowship mood of the evening as part of a day's work. "This simply gives the diplomatic representatives an opportunity to become acquainted with the Washington leadership. That's all," observed David M. Thomas, the Liberian ambassador to the United Nations.

Some of the Washington faces didn't need an introduction. Adriaan Eksteem, a South African representative, had lived in Washington between 1968 and 1973. "It's interesting to talk about Washington's progress from nonrepresentational to a delegate in the House," said Eksteem. "And of course I've known who Mr. Hechinger was for a long time. I've spent many Saturday mornings in his store."

The only direct politicking of the evening came from Hechinger, who announced he was "considering bringing the case of Washington before the Committee of 24," the U.N. body that deals with decolonization. His remarks prompted an informal, admittedly unrealistic strategy session between West German Ambassador Rudiger Von Wechmar and Fauntroy. "John and Andy scored all our points for us tonight," said Fauntroy. "I didn't need to lobby for anything." CAPTION: Picture, Kurt Waldheim with Marion Barry, by AP