Members of the largest Korean community in the United States demonstrated today against the reported Soviet destruction of a Korean Air Lines jetliner, but the firmly anti-communist South Korean immigrants said they wondered if the government of their adopted land would do much about it.

"We have been most disappointed in the past," said Chang B. Moon, a community leader whose sister was among the 269 people, including more than 70 Koreans, believed dead after the 747 jet apparently was struck by a Soviet missile. "We like to settle all these problems with idealism . . . . But the Russians won't buy idealism, they will only buy strength."

About 400 Korean immigrants marched in front of the Los Angeles Federal Building for an hour, singing the Korean national anthem and carrying signs saying "Stop Russian Barbarians" and "Bloodthirsty Pirates."

Almost all the men who came here as adults said they were veterans of the South Korean army. Many said America had responded too weakly in the past to events like the Soviet invasion of Afghanistan. "The U.S.A. is too soft," said Joon Rho, a biochemistry professor at the University of Southern California who has lived here 24 years. "The Communists are really barbarians. What they say and what they do is very different."

Moon, 41, president of the Korean Chamber of Commerce for Southern California, said he felt "shock and emptiness" when he learned he had lost his sister Youngjam Sohn, 48. He said he hoped the incident would "convince the American people that they cannot rely on peaceful coexistence."

Twenty years ago, Rho said, no more than 4,000 persons of Korean descent lived in Los Angeles, but today an estimated 250,000 of the 700,000 Koreans and Korean-Americans in the United States reside here.

Relaxed immigration laws have brought an enormous influx in the last decade. What was once a multiracial neighborhood of apartments and small shops four miles west of downtown Los Angeles has become a Korean enclave. It has been given the height of southern California recognition, a new freeway sign saying "Koreatown Next Right".

Koreans here retain many ties to their homeland, and many knew people on the downed flight. Ho Min Kim, owner of the East West Food Center on 8th Street, had gone to high school in Seoul with the pilot, Capt. Byong In Chun. The sister of Suk Park, 26, a garment worker at today's demonstration, was a stewardess on the plane. "She often talked about her concern, flying so close to Russian territory," said Park's husband, Yong, as they held "Stop Trade With Russia" signs.

Many Koreatown residents said they were enraged by suggestions that the plane was on an espionage mission, or that the pilots failed to heed Soviet warning signals. "The Korean Air Lines pilots used to be air force pilots," said Chul Lee, editor-in-chief of the Los Angeles edition of the Korean Times. "They are very alert, and very cautious. We Korean people, we know what the communists will do, but the American people still don't understand."

A similiar demonstration of about 300 occurred in San Francisco.