One year after a Korean Air Lines 747 jet was shot down by a Soviet fighter, killing all 269 people aboard, families of the Japanese victims continue to press for compensation and further investigation of the incident.

The South Korean and Japanese governments, however, are showing signs of wanting memories to fade and are cautiously resuming overtures to the Soviets that were suspended in protest when the jet was destroyed over the sea off Sakhalin Island.

The 747, operating as Flight 007 from New York to Seoul, was downed by an air-to-air missile after flying through Soviet airspace for several hours on Sept. 1, 1983. U.S. and South Korean officials have blamed the intrusion on a navigational error.

The Soviet media, meanwhile, have marked the anniversary with repeated articles elaborating on Moscow's contention that the jet was conducting a spy mission for the United States over important military installations.

In Japan and South Korea, family members plan ceremonies Saturday to memorialize the dead. About 90 people are scheduled to take a boat from a Japanese port to within 20 miles of the small, Soviet-administered island of Moneron near the impact point and hold a service at sea.

In South Korea, a memorial ceremony and the unveiling of a monument will mark the loss. About 85 Americans are expected to attend, many of them flown free of charge by the airline. The monument will stand on a hill 60 miles south of Seoul that has a name that translates as Homeland Longing Hill and is a special cemetery for Koreans who die overseas.

"All I can do now is to pray that the soul of my husband may rest in peace," said Kim Ok Hee, wife of the downed jet's captain, Chon Byong In. "My heart aches every time I hear my son saying he would like to become a pilot."

At a press conference in Tokyo today, representatives of victims' families and left-leaning legislators announced formation of an association aimed at bringing about further investigation into the jet's downing.

"The fact that the plane was shot down by the Soviets has been much played up, but the reason why the plane violated Soviet airspace has not been fully pursued," said Hideyuki Seya, a senator who belongs to the Japan Socialist Party.

One group of families here has sent monthly letters to President Reagan claiming the United States shares in the responsibility. They say the letters have never been answered. The Soviet Embassy in Tokyo, meanwhile, has refused to accept similar letters directed at officials in Moscow.

Families representing 26 of the 28 Japanese victims are about to file a joint lawsuit for compensation in a Tokyo court and are reportedly leaning toward alleging that the jet deliberately violated Soviet airspace. They are seeking a total of $2.75 billion.

South Korea has no diplomatic relations with the Soviet Union. Prior to the KAL incident, however, Seoul had been making unofficial contacts with Moscow as part of a general diplomatic campaign to improve relations with communist countries. After the jet's downing, these efforts were suspended.

On Saturday, South Korea said "We take this opportunity to urge the Soviet authorities once again to take appropriate measures" to compensate victims, Reuter reported from Seoul.

In June, South Korean Foreign Minister Lee Won Kyung indicated his government was ready to resume unofficial contacts. Seoul officials have said that world condemnation and the International Civil Aviation Organization's adoption of a resolution banning use of weapons against civilian planes had made their point sufficiently.

Earlier this month, a professor from the state-run Seoul National University was allowed to attend an international map commission meeting in Moscow. Seoul has also invited a Soviet Olympic official and a journalist to attend opening ceremonies a month from now for a stadium South Korea will use in hosting the 1988 Olympics.

Seoul officials, meanwhile, report that numerous changes in equipment and training have been implemented in response to Flight 007's fate. In February, a communications center opened at Seoul's Kimpo Airport that for the first time allows direct communication with all Korean Air Lines jets.

A $15 million flight simulator purchased recently has resulted in the grounding of 14 pilots, according to officials. In general, they say, safety inspections and training have been upgraded.

Japan has long since lifted minor sanctions it imposed against the Soviets. They included reducing Japan Air Lines' flights to the Soviet Union and the Soviet carrier Aeroflot's to Japan and banning Japanese officials from using Aeroflot.

Foreign Ministry officials here say Japan is attempting to resume a dialogue with the Soviets. A confidant of Prime Minister Yasuhiro Nakasone, Yoshio Sakurauchi, is currently visiting Moscow for discussion of undisclosed subjects.

Defense analysts here say the incident underlined strengths in Japan's electronic intelligence facilities. They monitored the Soviet fighter pilots' radio conversations and presented proof to the world that the pilots had shot down the jet. But, analysts say, they were slow in getting that information to the top of the command structure.

Politically, the incident probably strengthened Nakasone's hand in his efforts to increase Japan's military spending. And for the first time, Japan now has a Cabinet-level officer in charge of crisis management.