The Reagan administration is quietly prodding other nations to take concerted action "spontaneously" to restrict Soviet commercial aviation in retaliation for shooting down a South Korean airliner, official sources said yesterday.

"What the United States can do unilaterally doesn't amount to a hill of beans," an administration official said. "This incident won't amount to anything unless other nations decide to act."

President Reagan will try to galvanize the international response tonight with a nationally televised speech from the Oval Office in which he is expected to ask for reparations for the families of the 269 people who died after the Korean Air Lines 747 was struck by a Soviet heat-seeking missile.

Reagan described the downing of the airliner as a "barbaric, uncivilized, cold-blooded act" in a meeting with congressional leaders yesterday.

Though the president plans to use similar, blunt language in his 8 p.m. speech, he is expected to make his appeal for international restrictions indirectly, if he refers to such restrictions at all.

One official said that the administration is seeking "synergistic activity" in which a number of nations respond simultaneously and expressed the view that the United States must be "a delicate actor" in the process.

"We have started the wheels in motion to isolate the Soviets from an aviation standpoint," a senior administration official said.

The administration already has consulted with the British, Dutch and other western European governments as well as with the Canadians and the Japanese in an effort to promote international action aimed at restricting Soviet landing rights in other countries for no more than 90 days, officials said.

The United States suspended all Aeroflot commercial flights to this country in December 1981 in retaliation for Soviet repression in Poland, and does not contemplate restricting the airline's few remaining diplomatic flights to this country.

The most punitive options open to the administration have been ruled out. Reagan said Saturday that he will not approve any slowdown in arms-control negotiations, and White House spokesman Larry Speakes reiterated again yesterday that the United States will not renew economic sanctions against the Soviets.

Reagan's theme, repeated again and again by administration officials during the past two days, is that the issue should be cast as "the Soviet Union versus the world" rather than as a conflict between the Soviet Union and the United States.

By this stance the administration hopes to isolate the Soviets for what Reagan told the congressional leaders was "an affront to humanity" and to encourage actions by nations that usually try to stay out of disputes between the superpowers.

In an effort to demonstrate Soviet callousness, sources said, the United States will release at the United Nations early this week transcribed tape recordings of the in-flight conversations of Soviet pilots in the moments before the Korean airliner was shot down.

The United States also is expected to back a move in the International Civil Aviation Organization, a U.N. agency based in Montreal, to condemn the shooting and to improve warning measures to prevent airliners from straying over Soviet territory. Korean Air Lines flight 007 was more than 300 miles inside the Soviet Union when it was shot down.

Officials said that unilateral actions likely to be taken by the United States though not necessarily announced by Reagan tonight include "foot-dragging" on reopening negotiations on cultural and scientific agreements that had been expected to be approved by Washington.

The congressional leaders who consulted with the president and high administration officials for an hour and 40 minutes yesterday were generally supportive of the administration's planned reaction to the incident.

They said they also expect Congress to pass a resolution condemning what House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) called "heinous, horrible murder."

But some senators and some conservatives outside Congress expressed concern that administration actions have failed to match the president's strong rhetoric.

"The administration has always used tough words," said Sen. Daniel Patrick Moynihan (D-N.Y.). "What tough things has it done? What the Soviets will look at is what what they call 'objective reality.' Have you agreed to feed our army or have you not? Have you given us credits or have you not? Have you agreed that we abide by the Helsinki accords or have you not?"

But Moynihan, appearing on "This Week With David Brinkley" (ABC, WJLA), said that he is prepared to follow the president, if Reagan is willing to lead.

Senate Minority Leader Robert C. Byrd (D-W.Va.), who after the incident called for cancellation of the recently negotiated grain agreement with the Soviet Union, said he raised the issue at the White House yesterday and got "no response." Byrd added that he did not now think that such action would be effective unless other grain-supplying nations joined in a boycott.

Two conservative leaders were more severe in their criticism.

Speaking at a news conference soon after Reagan met with the congressional leaders, Howard Phillips, national director of the Conservative Caucus, referred to Reagan's response thus far as "a disgraceful reaction."

Paul Weyrich, director of the Committee for Survival of a Free Congress, joined Phillips in urging that Reagan close U.S. ports to Soviet ships, cancel all arms control negotiations, expel Soviet diplomatic personnel and void the grain agreement.

In Dallas, Rep. Carroll Hubbard Jr. (D-Ky.) said the United States should prohibit U.S. airlines from flying to Moscow and ban travel from the Soviet Union. Hubbard had been scheduled to take flight 007 but took a different plane.