With a wave of anti-Soviet sentiment sweeping this country, South Korea today launched an international campaign to force the Soviet Union to apologize for the reported shooting down of a Korean Air Lines jumbo jet and to pay compensation for all losses.

Foreign Minister Lee Bum Suk issued his government's first formal list of demands against the Soviets and called for the United Nations Security Council to enforce those demands.

In addition to apologizing and paying compensation for the 269 passengers and crew members on board who are presumed dead, the Soviet Union must also punish those responsible for the plane's reported downing and give guarantees that such a tragedy will not be repeated, Lee said at a news conference today.

Meanwhile, search efforts continued in the waters off Sakhalin Island where the giant airliner disappeared early Thursday morning. The United States, Japan and South Korea have charged it was knocked from the sky by a Soviet fighter plane, but the Soviet Union has not admitted to shooting it down.

Japanese military radar controllers have said the plane, bound from New York to Seoul, wandered far off course and flew over Sakhalin, which is heavily fortified Soviet territory north of Japan.

Foreign Minister Lee today gave his government's first acknowledgment that the plane had been off course and had passed over Sakhalin. But he offered no explanation for that detour. Whatever the reason, Lee said, the downing of an "unarmed passenger plane is inexcusable."

The government served notice it would attempt to rally international opinion behind a strong denunciation of the Soviets. Ambassadors assigned here were urged to support the South Korean position at the United Nations and in other international forums.

President Chun Doo Hwan urged Japanese cooperation in pressing for United Nations action during a telephone conversation today with Japanese Prime Minister Yasuhiro Nakasone, government officials said.

Tonight, Chun also cabled President Reagan, calling the Soviet attack an "inhuman and barbarous action" that should be condemned by the whole world.

It is now presumed here and in Tokyo that all aboard the plane died. Kerosene patches on the waters north of Japan have been spotted by search crews but no survivors have been sighted.

Japanese military radar had reported spotting what appeared to be fighter planes on the scene shortly before the plane suddenly disappeared from radar screens.

Japanese military intelligence also monitored Soviet radio communications that indicated an attack was taking place.

According to the Asahi newspapers in Tokyo, Japanese military sources said the following sequence of words in Russian was overheard.

"Take aim at the target."

"Aim taken."

"Fire."

"Fired."

The downing of the plane is certain to chill relations between Japan and the Soviet Union even more than in the past. For at least five years the Japanese have complained of the Soviet fortification of one of the Kurile Islands north of Japan not far from Sakhalin and also of the increasing presence of Soviet aircraft near the Japanese mainland.

The affair also has wrecked the modest beginnings of better relations between South Korea and the Soviet Union, which do not formally recognize each other. South Korea has hoped for cultural and trade exchanges with the Soviets and had been hoping that Soviet athletes would come to Seoul for the 1988 Olympic Games.

But those faint feelers appeared to have been swept away as South Korea turned on a burst of anti-Soviet demonstrations today. There were rallies in high schools throughout the country, obviously with government approval. Students shouted slogans denouncing the act as "inhuman" and "barbarous." In Pusan, students in an anticommunist league donned headbands bearing the single word "condemn."

The government-controlled television network aired interviews with outraged Koreans throughout most of the day.

The government appointed a task force to handle all aspects of the incident. It is headed by Minister of Transportation Lee Hi Sung, a former general.

The government plans to stage a massive memorial on Sept. 7 at Kimpo International Airport, where the ill-fated airliner was supposed to have landed at 6 a.m. Thursday. At least 82 Korean passengers were aboard along with 29 Korean crew members.