Bills in Congress to impose strict import quotas on Japanese cars will be shelved because of the voluntary limits set by Japan, the chief sponsor of such legislation said yesterday, even though the promised cutback in car shipments is much smaller than the auto industry and its political supporters had been pressing for.

Sen. John Danforth (R.-Mo.) said he doesn't plan to proceed with his quota legislation, assuming that the details of the Japanese plan match the initial reports. The voluntary limit imposed by the Japanese government on its auto companies would hold car shipments to the United States to 1.68 million units during the 12-month period beginning April 1.

"Although I personally think that greater concessions should have been made, I believe the Japanese plan is an important step in the right direction," said Danforth. His bill would have forced a bigger cut in imports from Japan, and for three years, not one.

Two of the hardest-hit U.S. companies, Ford Motor Co. and American Motors Co., took the same position yesterday, recognizing, as one auto company official said, that the voluntary agreement was the best they could hope for now. Industry analysts said it would provide little immediate help to Ford, AMC and Chrysler Corp.

"This isn't all we wanted, but it is significant; it is helpful," said Sen. Lloyd M. Bentsen (D-Tex.). "We will, however, be watching next year to make sure they are complying," said Bentsen, a co-sponsor of the danforth bill.

The Detroit automakers were not overjoyed, however, nor were some of their defenders in the Michigan congressional delegation. Sen. Donald W. Riegle Jr. (D-Mich.) called the import limit "a victory of sorts," but added that he is concerned about possible "loopholes" that would permit Japanese car sales to exceed the new limit substantially.

However, one of Riegle's aides said the senator would not continue to push for legislated import quotas this year.

The first-year limit of 1.68 million passenger cars would be followed by a ceiling of 1.82 million during the year beginning April 1, 1982, but Japan could increase shipments above that level if sales of U.S. autos improve significantly in 1982, U.S. officials said.

The cutback would reduce Japanese exports about 140,000 below last year's total, according to U.S. officials. This would be a reduction of just under 8 percent, as the Japanese calculate export statistics. Danforth said the cutback could be as great as 250,000 autos over the next year, depending on overall U.S. car sales.

"The symbolic gesture is significant, but the numbers don't add up to much relief," said Rep. James J. Blanchard (D-Mich.). "You've got to get to 1.2 million or 1.4 million before you really feel the restraint."

Ford Chairman Philip Caldwell, who had led the industry's pleas for import relief, was studiously neutral in his response. "Restoring the health of the U.S. auto industry in clearly an essential ingredient of the president's economic recovery program. Voluntary import restraint by the Japanese will make a contribution to that end, and we welcome a disposition of this matter," Caldwell's brief preapred statement said.

American Motors Chairman Gerald C. Meyers called the action "a step forward." General Motors, the only one of Detroit's Big Three automakers to show a profit in the first quarter, said it was pleased that the voluntary limit would prevent legislation.

Ford officials previously had said that the economic gains from a limit of 1.6 million cars would be meager. If Japan's shipments to this country were reduced by 140,000 over the next year, Ford's sales could grow by between 30,000 and 40,000 cars, boosting its cash flow by perhaps $60 million, according to industry analysts. That would be welcome, but not a cure-all for the No. 2 automaker, which had a loss of $439 million in the first three months of the year.

The White House described President Reagan as pleased at the outcome, saying the voluntary limit "will go a long way toward eliminating the need for congressional action" and "will give the U.S. auto industry time to retool and become competitive," according to press spokesman Larry Speakes.

Speakes also said the administration is "hopeful" that the limit on Japanese autos will not lead to higher new-car prices in this country. That result was predicted yesterday by Robert M. McElwaine, president of the American International Automobile Dealers Association, whose members sell Japanese and other foreign cars. "I'm sure that a car that was discounted $200 or $300 yesterday won't be discounted today," he said, assuming that a tighter supply will permit higher prices.

"You've already seen some of the impact in the otherwise inexplicable price increases this week by the U.S. manufacturers," he said.

In the longer run, the congressional mood will depend on how deeply the voluntary trade limit bites into Japan's auto exports.

The 1.68-million-car limit apparently does not include the approximately 400,000 unsold Japanese cars that are already in the United States, congressional aides said. Nor does the agreement cover Japanese shipments to Puerto Rico, which totaled just over 65,000 last year, or a lesser number of four-wheel-drive wagons that Japan classifies as trucks but the United States counts as cars, U.S. trade officials said.

But the restraint would become increasingly significant if U.S. car sales recovery strongly from the deep slump of the past 18 months. Allen Sinai of Data Resources Inc., an economic forecasting firm, noted that cars are currently selling at an annual rate of just over 9 million units, close to last year's depressed figure. But the annual sales rate could improve to the 10-million level by the final quarter of 1981 if the economy improves, and at that point the import restraints begin to help the American industry, he said. t