U.S.-Soviet relations yesterday took on a new layer of frost as the State Department barred Soviet Foreign Minister Andrei A. Gromyko from landing at any U.S. civilian airport and the two countries sparred on a wide range of matters previously considered routine.

State Department officials backed up the refusal by the governors of New York and New Jersey to allow a special Soviet flight to land at New York-area civilian airports to bring Gromyko to the fall session of the U.N. General Assembly.

The State Department said Gromyko would be permitted to arrive only on a "non-civilian" plane and would be required to land at an undetermined military airport.

It was still unresolved late yesterday exactly how Gromyko would arrive for his annual visit to the United Nations.

At White House direction, administration officials were seeking to avoid allowing Aeroflot, the Soviet airline, to land even a plane full of diplomats here during a period when many non-communist nations have barred Aeroflot flights to protest the Soviet downing of a South Korean jetliner carrying 269 persons.

In other signs of continuing fallout from the Sept. 1 Korean Air Lines disaster:

* By 26 to 2 the International Civil Aviation Organization (ICAO) adopted a resolution "deeply deploring" the Soviet destruction of a civilian jetliner and ordered its own investigation. Only the Soviet Union and Czechoslovakia voted no.

* The Soviet government abruptly recalled 20 Soviet scholars in the United States for a year of study at American universities, saying it feared for their safety in the current anti-Soviet atmosphere.

It was the first such incident in 25 years of U.S.-Soviet academic exchanges, and State Department officials said it would leave no Soviet citizen in this country under long-term exchange agreements.

* U.S. officials attempted for the second time this week to give the Soviets two diplomatic notes demanding compensation for the Americans and South Koreans killed aboard the KAL flight.

The second-ranking diplomat at the Soviet Embassy, Oleg Sokolov, again refused to accept the notes from Assistant Secretary of State Richard R. Burt, even after Burt warned that such refusal could lead to serious repercussions.

* Administration officials continued to debate whether to cancel a tentatively scheduled Sept. 27 meeting between Gromyko and Secretary of State George P. Shultz, who sharply criticized the Soviet foreign minister after their last meeting in Madrid.

* The State Department's top East-West trade expert, William A. Root, resigned--but then reconsidered his resignation--in a dispute over whether to give the Defense Department veto power over sales of oil and gas exploration equipment to the Soviet Union.

* Scattered local protests persisted across the country, ranging from the refusal of West Coast dockworkers to unload Soviet cargo to a California legislative resolution urging that Soviet athletes be barred from the 1984 Olympic Games in Los Angeles.

Earlier this week, the State Department sought permission for Gromyko's special flight to land at Kennedy or Newark airports in the next few days. But New York Gov. Mario M. Cuomo (D) and New Jersey Gov. Thomas Kean (R) ordered the region's Port Authority to reject the request, saying the landing could trigger public demonstrations.

"We can find no justification for endangering our people and placing enormous strains on the police and security forces of the two states just to accommodate Soviet diplomats," Cuomo said.

Gromyko usually travels abroad in a four-engine IL62 with Aeroflot insignia on its side. Such flights are not considered regular commercial runs and were not halted by President Reagan's January, 1982, decision to deny Aeroflot U.S. landing rights, a position that Reagan reaffirmed after 269 people were killed aboard the South Korean airliner.

Such an Aeroflot plane presumably would be barred by the State Department's edict, which was conveyed to Sokolov yesterday, that Gromyko would have to use a "non-civilian" aircraft and at a U.S. military base.

This left the unprecedented possibility that Gromyko might land in a Soviet military jet at a U.S. military airfield, probably McGuire Air Force Base, 75 miles southwest of New York.

A State Department spokesman said the United States was required as the host country for the United Nations to facilitate Soviet travel to the U.N. General Assembly.

"We intend to act in accordance with our international obligations, even if the Soviets violate theirs, as in this case," the spokesman said.

Outside Washington, people protested the death of the 269 persons in various ways. Bar owners in Boston, for example, dumped Soviet vodka into the harbor in scene reminiscent of the Boston Tea Party. Several state-run liquor authorities already have banned the sale of Soviet vodka.

The Soviet freighter Novokuibyshevsk was unloaded in Ensenada, Mexico, after workers in Los Angeles refused to unload the ship for six days. Officials at the International Longshoremen's Association, which had unloaded tractors from a Soviet ship in New Orleans under 24-hour security, said they had to unload the cargo to avoid jeopardizing millions of dollars in contracts.

The California Legislature unanimously passed a resolution urging Reagan and Congress to bar the Soviets from the 1984 Olympics. "We feel it's appropriate to take some concrete action against the Soviets," said the sponsor, state Sen. John Doolittle (R). "The Soviets prize participation in the Olympic Games more than any other activity."

But F. Don Miller, executive director of the U.S. Olympic Committee, said this was a "narrow-minded" effort that recalled the U.S. boycott of the 1980 games in Moscow.

"It's a sorry state of affairs that we do not have men with enough intellect to develop a foreign policy with some meat in it, but go back to the same thing again and again," Miller told the Associated Press. "Isn't there more to our foreign policy than amateur sports?"

On Capitol Hill, meanwhile, several conservatives called for a tougher U.S. response to the airliner incident, such as restricting the flow of advanced technology to the Soviet Union.

James Dunne II, chairman of the International Airline Passengers Association, told Rep. Philip M. Crane (R-Ill.) at a hearing that the Soviet action had set a precedent for the shooting down of unarmed passenger planes.

"Worldwide government and aviation leaders must immediately adopt rules, sanctions and policies to protect the safety of the traveling public and to ensure that this kind of terrible tragedy will never happen again," Dunne said.

But Assistant Commerce Secretary Lawrence J. Brady said that Reagan has been "quick to speak out forcefully in condemnation of this terrible deed."