Norwegian Defense Minister Johan Holst spent yesterday at the White House, the Pentagon and Congress, trying to calm the storm over his country's role in helping the Soviet Union make its submarines so quiet that they are now difficult for the United States to detect.

But he failed to head off a growing congressional effort to pass punitive legislation, Sen. Jake Garn (R-Utah), sponsor of one of the toughest measures, said last night after meeting with Holst.

Garn has proposed an amendment to the Senate trade bill that will attempt to close the American market to any foreign firm that sells sensitive technology to Warsaw Pact nations. A Senate vote on the bill is expected next week.

"They {the Norwegians} have done far more than the Japanese" to prevent a recurrence of the high-tech sales, which enabled the Soviet Union to manufacture a new generation of submarine propellers which make less noise, Garn said. "But I'm still going ahead with my amendment."

Holst told The Washington Post that he had stressed in his meetings with U.S. officials that Norway is reorganizing its government bureaus to guard against a future technology breach. "This whole question of antisubmarine-warfare is as much a concern for the Norwegians as for the Americans," he said.

The ban proposed by Garn might bankrupt Norway's Kongsberg Vapenfabrik firm, Holst said, because it depends heavily on sales of its Penguin antiship missile to the Pentagon. Kongsberg and Japan's Toshiba Corp., an electronics giant, supplied the Soviet Union with sophisticated, computerized milling machines that enabled the Soviets to manufacture submarine propellers which emit very little noise, according to the Reagan administration. Until that advance, Navy officials say, the United States had little trouble keeping track of every Soviet sub.

But with the new propellers, Soviet subs have become so quiet that the United States would need to invest billions of dollars to develop and deploy improved antisubmarine systems, according to the Pentagon. The United States already has spent billions installing listening gear on U.S. submarines that track their Soviet counterparts, and deploying such equipment on ocean bottoms.

"It was unquestionably a serious breach which will cost us billions to counter," Fred C. Ikle, undersecretary of defense for policy, said yesterday. "We are talking with both governments to work out arrangements" to tighten export controls on high-tech equipment. The Norwegian and Japanese firms circumvented longstanding NATO export controls aimed at barring such machinery from Warsaw Pact nations.

Holst met yesterday with Deputy Defense Secretary William H. Taft IV, White House national security adviser Frank C. Carlucci and Garn, according to the Norwegian Embassy. After the Holst-Taft meeting, the Pentagon issued a short statement noting the two had agreed "on the seriousness of the situation and the damage done to our mutual security" and the need to cooperate "to overcome the damage," including the completion of civil and criminal investigations in Norway.

Garn is one of several members of Congress backing punitive legislation for such security breaches. Pentagon officials said yesterday that they want such legislative weapons on the books, but are not yet ready to endorse any of the bills now before Congress.