A South Korean passenger airliner that strayed into a Soviet strategic air defense zone ignored orders to land, and flew over the Soviet Union for two hours before Mig fighters firing on the plane forced it to make a nighttime crash landing on a frozen Arctic lake, officials said yesterday.

The Soviet Union informed U.S. officials that two of the 110 persons aboard the Korean Air Lines 707 had been killed and another 13 injured, two of them seriously, but provided little other detailed information.

The bizarre incident - which saw the Korean airliner, on a regularly scheduled flight from Paris to Anchorage, Alaska, make a U-turn over the North Pole and fly 1,000 miles into Soviet air space - left a number of key questions yet to be answered.

Was the Boeing jet so far off course as a result of some incredible navigational failure, or was it possible - as sources in South Korea suggested - that the plane had been hijacked?

Why would the pilot of the Korean plane - as the Soviets charge - ignore repeated signals by Soviet jet interceptors to follow them down to an airfield, and try instead to evade them for two hours before he was finally forced down?

Did the Soviet Mig interceptors - which, according to President Carter's national security adviser, Zbigniew Brzezinski, fired at the Korean airliner - hit the plane?

Were the deaths and injuries reported by the Soviets caused by Soviet gunfire or by the hard landing that sheared off a wing of the plane and shattered the ice on the lake? Or perhaps in a battle aboard the Korean plane with a hijacker or hijackers?

How did the passengers and crew escape from the plane, and survive in the Arctic cold until their rescue?

The answers to these questions seemed likely to remain a mystery until the passengers and crew of the Korean airliner are released and flown out of the Soviet Union.

The Soviet Union, for its part, seemed eager to see the passengers depart, and the episode closed. The Soviet news agency Tass said arrangements were being made for "their departure from the U.S.S.R's territory."

The U.S. Embassy in Moscow reported last night that the Soviets had offered to allow an American civil airliner to land at Murmansk to retrieve the survivors, and sources suggested that an American airliner might be sent to fly them to Helsinki, Finland, today.

Another Korean Air Lines 707, bearing medical teams and the president of the airline, was reported en route from Seoul to Hesinki.

Despite the fact that no Americans were reported to be among the passengers aboard the plane, the United States has been involved in the negotiations because the Soviet Union does not recognize the South Korean government, and has no diplomatic relations with Seoul.

The downed plane, Korean Air Lines Flight 902 from Paris to Seoul with a refueling stop in Anchorage, was flying a trans-polar route and was well to the north of the Soviet Union when it made a sweeping turn.

According to Tass, the plane entered Soviet air space while "flying from the Berents Sea in a southern direction," and "penetrated deep over Soviet territory" northeast of Murmansk, the principal northern Soviet seaport.

This area, according to Western defense sources, is studded with anti-aircraft installations since it is near the border with Norway, a NATO nation. Soviet naval and rocket forces are concentrated in this area in large numbers.

Tass said that Soviet fighters, "in nighttime conditions, using [wing movements] of the planes and onboard lights, repeatedly issued orders to the intruder to follow them to land at some nearby airfield. The plane, however, did not respond to these orders."

Instead, according to State Department spokesman Tom Reston, Soviet officials informed the United States that the Korean airliner took "evasive action."

It was not known at exactly what point the Soviet interceptors opened fire on the airliner, or how many bursts were fired.

Tass implied that it was the plane's crew that ultimately decided to try to set the four-engine jetliner down on a remote, frozen lake near the settlement of Kem - 600 miles north of Moscow - in the darkness of Arctic night.

Lakes in this region are still frozen to a considerable depth at this time of the year, but also are covered with snow drifts and are used only as emergency landing strips by light Soviet aircraft.

Japanese sources in Moscow said the Soviet Foreign Minister informed them that the impact of the Korean airliner's landing shattered the ice, and that a wing was sheared off the plane.

No details were available on how survivors got out of the aircraft, or how long it took Soviet rescue workers to reach the scene. The survivors were initially taken to Kem.

Soviet authorities shed no light on what might have caused the Korean airliner to be hundreds of miles off course.

Korean aviation officials initially raised the possibility of navigational difficulties. The trand-polar routes bring planes close to the magnetic North Pole, which can cause wild deviations in conventional compasses.

But airline officials in Seoul later said a navigational error of the magnitude involved in this case was "unthinkable," and suggested that there may have been a hijacking attempt. This could also account for the failure of the pilot to heed Soviet orders to land.

Airline officials in Paris said the plane carried a South Korean crew of 13 and 97 passengers - 35 Koreans, 51 Japanese, five French, two British, two West Germans and two believed to be Chinese. The Soviets reported that one of the dead persons was Japanese. tic relations with the Soviet Union.

Since South Korea has no diplomatic relations with the Soviet Union, U.S. and Japanese authorities pressed the Russians for information about the plane for more than 12 hours before receiving any firm information.

The four-engined Boeing, a standard passenger jet in world service for almost 20 years, departed from Paris Thursday morning and was scheduled to make its rrefueling stop at Anchorage nine hours and 20 minutes later, and then continue on to Seoul.

When the plane failed to arrive, a search was launched in northern Canada. The effort was called off by the Canadians after they received information from the United States that the aircraft was down on Soviet territory.

Earlier this month, well to the south of where the jetliner was finally forced down, two Swedes were arrested by Finnish authorities after apparently flying a light plane onto a small frozen lake near the Finnish border north of Leningrad in what was later described as an unsuccessful attempt to help three women escape the Soviet Union.

Some sources here suggested that Soviet embarrassment over that incident, in which the plane apparently flew in and out of Russia without detection by radar, may have contributed to the aggressive response of the defense forces to this incident.