The House, by a 326-2 vote, passed a bill Monday granting health benefits to service veterans who participated in U.S. atomic weapons tests. The measure does not help civilians downwind from the test sites who may have been exposed to higher levels of radiation than the military personnel.

The bill affects about 250,000 servicemen and women who were, after World War II, either at the sites that were bombed in Japan, or participated in tests in the Pacific or in Nevada.It declares as "service-connected" a list of certain illnesses and thus would grant those affected veterans medical benefits.

The VA has said there is no scientific evidence that the present illnesses of the men and women involved were caused by radiation.

The VA has advised President Reagan to veto the bill. The Senate passed it last week by a 48-30 vote.

Natives of Pacific islands used in the tests in the 1950s were granted almost $1 billion in aid two years ago under a compact between the United States and the island governments. A bill to help downwind civilians, mostly in Utah, Nevada and Arizona, is being drafted by Sen. Orrin Hatch, R-Utah, and Rep. Wayne Owens, D-Utah.

Studies of civilian exposure to test radiation has in some cases shown higher levels of fallout than those incurred by troops nearer the blasts received. Direct participants were often shielded from radiation, or were quickly moved if fallout clouds moved their way. Fallout from the blasts in most cases became heavier as the clouds moved away and the atomic debris cooled.

Hatch and Owens have indicated they have hopes that Congress may be more sympathetic to the downwind victims, but so far neither the House nor the Senate has approved any of several measures offered since 1979 to aid the civilian victims.

The U.S. Supreme Court declined to hear an appeal of a court case brought by the downwinders. Attorneys for those victims won a judgment in U.S. District Court in Salt Lake City, but lost in the 10th Circuit Court of Appeals. The courts said the United States is immune to such suits on the grounds that its actions during the tests were "discretionary powers."