A Reagan administration attack on the danger of excess salt in the American diet is making so much progress that a law may be unnecessary, Food and Drug Administration Commissioner Arthur Hull Hayes Jr. said yesterday.

By the end of the year, between 33 and 50 percent of the canned, processed and packaged foods that the FDA monitors will bear labels revealing their sodium content, the FDA chief told an American Medical Association conference here. This is up from 13 percent a year ago and 7 percent about three years ago, and "clearly" should reach 75 percent in a few years, Dr. Hayes predicted.

The increase is due in large part to the FDA's aggressive campaign to have the food industry voluntarily label the sodium in foods while publicizing the dangers of too much salt in the diet.

The FDA regulates all processed foods except meats, where the Agriculture Department is urging similar labeling.

Americans consume two to four times as much salt as they need, surveys show. One apparent result, though cause and effect remains unproved, is millions of cases of high blood pressure, which often leads to strokes or heart disease.

High salt intake can also make high blood pressure worse. Many foods, even supposedly "unsalty" ones like ice cream, peanut butter and gelatin desserts, contain added salt, its presence often undisclosed.

The AMA, concerned with what it calls this "devastating" health problem, voted in December, 1979, to back mandatory labeling of foods' sodium content by some "cost-effective" means. It testifed last year in favor of such legislation, but a sodium-labeling bill in the House failed to get out of committee.

Labeling alone will not solve the excess-sodium problem, Hayes and Dr. Lowell Steen of the AMA board of trustees agreed. Both called for public education to make the public, in Hayes' words, "as conscious of sodium intake" as of calories. Other goals, he said, are to reduce the sodium added to foods and to get more low-sodium foods on the market.

A clear sodium-content label is essential, Hayes said, as is public understanding that "salt" or "salts" can be present in many guises. They are present in any product that has "sodium," "monosodium," "disodium" or "trisodium" as part of the chemical name.

Hayes said the FDA will issue a formal, still tentative proposal "in the next few weeks" that might eventually require processors to add sodium content if they already print a "nutrition label," which lists calories and other information. It would allow a processor to claim "reduced sodium" if present content were cut by three-fourths.

Hayes called this a reasonable reduction for significant numbers of now highly salted canned soups and vegetables, frozen foods, snacks, some cheeses and some "fast foods," ranging from pizzas to fried chicken to french fries.