On Wednesday morning last week, a State Department protocol officer telephoned Kennedy International Airport to make arrangements for the Soviet Union to land a special diplomatic flight bringing Foreign Minister Andrei A. Gromyko to the U.N. General Assembly.

About an hour later an airport official, Donald R. Burns, called back to say this would present serious problems and to suggest that Gromyko land at a U.S. military base instead.

This brief telephone exchange was the beginning of a process of discussion and decision that erupted in international controversy several days later, resulting in Gromyko's cancellation of his annual trip to New York and a Soviet verbal blast at the United States.

The incident and its repercussions have affected Soviet-American relations, the East-West political climate and the status of the United States as host country to the United Nations. But interviews with those involved suggest that public and political sentiment, rather than such big international questions, were the central elements in the decisions in New York and in Washington.

Burns, who is the manager of the Kennedy airport's public services division, said he knew immediately that "security and safety" problems would be presented by a Soviet aircraft landing with Gromyko amid widespread public outrage about the Soviet shooting down of Korean Air Lines Flight 007.

Making the request more complicated, Burns said, was that Aeroflot has been barred from regular operations at Kennedy since the Soviet invasion of Afghanistan, and the State Department was unable to say who would be responsible for ground handling of the plane after Gromyko came down the ramp.

Unknown to Burns, the ground-handling issue already was troubling the State Department. According to officials there, the department had decided earlier "at a high level"--but below Secretary George P. Shultz--to approve the special Gromyko flight, and had notified the Soviet Embassy the previous weekend.

But when State Department officials asked U.S. airlines to consider servicing Gromyko's plane on the ground at Kennedy, the reactions were wary to negative.

"They said tensions and feelings in New York were running very high," an official recalled.

After an inquiry from the State Department's Soviet desk late Wednesday, top officials of the Port Authority of New York and New Jersey, which operates Kennedy and other New York-area commercial airports, met the following day on the issue.

The decision, according to Peter C. Goldmark Jr., executive director of the Port Authority, was that "we would have a virtually impossible situation" if Gromyko landed at Kennedy.

The likelihood of major, perhaps massive, public demonstrations against Gromyko was one factor in this judgment. A less obvious but perhaps even more difficult problem was the strong emotion of Kennedy airport personnel, arising from the fact that they started the South Korean airliner on its ill-fated journey two weeks earlier.

To those who cleaned the KAL plane and processed the passengers at Kennedy, Flight 007 was not just a disembodied name but "a real plane with real people," said Goldmark.

"Generally and in most cases we follow without question requests of the federal government," Goldmark said. "They manage our foreign policy."

In this case, though, the Port Authority based its judgment on "safety and security," he said. "At best this would have been a very serious situation, at worst a disaster . . . . We all agreed that the answer was no." At 4 p.m. last Thursday the State Department was notified.

Washington, already alerted, had been working on alternate landing sites for Gromyko: Stewart International Airport, a former Air Force base now operated by New York state and a little over an hour's drive from Manhattan, or McGuire Air Force Base in New Jersey, about two hours' drive from Manhattan.

In view of the potential political impact, Goldmark also had notified the offices of governors Mario M. Cuomo of New York and Thomas Kean of New Jersey, who have a degree of control over the semi-independent Port Authority.

Cuomo decided "in a matter of minutes," according to an aide, that the flight should be forbidden and, moreover, that he should speak out publicly as a matter of "moral obligation."

Kean conferred with his staff for 90 minutes on the case, one of his aides said. "With the blood of innocent civilians on the hands of the Soviet government," Kean said later, he would not accept the Gromyko flight. The two governors made an announcement Thursday night.

The top level of the Reagan administration knew little or nothing about the problem until late Thursday, according to officials. But with the Port Authority rejection and the governors' public statement, it quickly became an urgent question.

Up to that point, nothing much had been said about the fact that Gromyko customarily travels in a special plane with the markings of Aeroflot, the Soviet airline. Now White House officials reportedly insisted that no Aeroflot plane should be permitted to land here, even at a U.S. military base.

The diplomatic argument was that an Aeroflot landing, even of a special plane carrying Gromyko, would contradict U.S. efforts to persuade other nations to ban landings by Aeroflot as a protest gesture to the downing of the Korean plane. It also seems clear that some people high in the administration wanted to appear at least as tough as the two governors.

The Soviet Embassy was informed by Assistant Secretary of State Richard Burt Friday morning that Gromyko would be permitted to land only in a "noncivilian aircraft" at a noncommercial airport. Shortly thereafter, the State Department announced this decision.

In speaking to reporters, and evidently in the conversation with the Soviets, officials justified the decision on "problem-solving" and practical grounds due to the governors' action. The usual State Department practice of seeking to assert federal authority over state authority in foreign policy matters was not followed.

Several officials experienced in Soviet affairs were not surprised that Gromyko refused to accept the flight restrictions, in view of the strained state of U.S.-Soviet relations and the importance of protocol in Soviet diplomacy.

That Gromyko so quickly canceled his trip Saturday morning, without seeking to contest or adjust the U.S. decision, suggested to some American officials that he was not enthusiastic about coming in the first place. He also had little time to decide whether to pack or unpack. His plane was due in New York Sunday.