President Carter yesterday rejected high tariffs on shoe imports to protect the American industry and instead said the administration would try to work out relief for the industry by negotiating voluntary quotas with South Korea and Taiwan.

The move was assailed by the shoe lobby and many legislators, who charged that such arrangements --called orderly marketing agreements --relief to the industry even if they can be reached.

The President's move was also another defeat for organized labor, which in recent weeks has lost a major congressional fight on construction site picketing and was rebuffed in a try to get the administration to recommend a big rise in the minimum wage.

The shoe industry backed the recommendations of the U.S. International Trade Commission, which proposed a 40 per cent tariff on imports that exceed 265 million pairs a year. Imports now have a 46 per cent share of the U.S. market.

The commission administers most of the nation's trade laws.

It is estimated that consumer costs for shoes would have increased by $300 million to $500 million annually if the commission's recommendations had been accepted by Carter. Most of that cost, according to retailers and Treasury officials, would have fallen on low-income families because they buy most of the low-cost shoes involved.

Robert S. Strauss, the President's top trade negotiator, said the decision will satisfy no one entirely but tries to balance free trade and inflation against domestic employment and output.

Strauss said he would visit Japan next week to discuss another pressing trade problem -- imports of color television sets. The trade commission has recommended higher tariffs on imported color sets.

Strauss said he met with members of Congress yesterday morning to tell them of the President's decision on shoes. He called it "the best solution available to a very difficult problem." He said the legislators, including House Speaker Thomas P. O'Neill (D-Mass.), "expressed their displeasure with this decision, and second they expressed their confidence in me, even though they were not thrilled with the first program I brought them."

Shoes imports to the United States increased by more than 100 million pairs, between 1974 and 1976, with most of the increase accounted for by South Korea and Taiwan.

But the last two years represent merely an acceleration of a long-term decline of much of the American shoe industry. Since 1968 the number of firms in the industry has fallen from 600 to 380 and 70,000 jobs have vanished.

The industry has sought import relief several times in the past, but has always been rebuffed.

Carter said he had taken the move to negotiate voluntary quotas reluctantly because he did not want "to restrict international trade in any way . . . Only problems as extreme as those faced by the American shoe industry could force me to seek even modest mandatory limits on imports."

The agreements would be in effect for no more than five years, Strauss said.

The President has before him major decisions on protecting American sugar growers and television manufacturers which he must make by early May.

Administration officials said that in view of the strong labor-industry pressures in the shoe decision, the compromise proposed by the President is the one least damaging to free-trade principles that has a chance of working politically.

But at any point in the next 90 legislative working days congress has the strict international trade in any right to overrule the President -- even while he is negotiating the voluntary quotas -- and impose the International Trade Commission remedy.

The administration has 90 days -- a shorter time period -- to negotiate the voluntary quotas. While Strauss said, the administration is already talking to Korean and Taiwanese officials, he said that agreements might have to be worked out with other major suppliers -- such as Brazil, Spain or Italy.

If voluntary arrangements cannot be worked out, Strauss said, then the President "still has the full range of options, including the trade commission recommendations. The only option he doesn't have is no relief."

Trade officials said the administration will seek to establish voluntary quotas somewhere between the 9 million pairs Korea shipped in 1974 and the 44 million pairs last year and for Taiwan, between the 88 million pairs it shipped in 1974 and the 156 million pairs shipped in 1976.

Last year the Ford administration worked out an orderly marketing arrangement with Japan on specialty steel imports, then imposed quotas on other major suppliers.

Carter also called yesterday for improved adjustment assistance to help industries, communities and workers to adapt to impor competition. He said that if need be, the administration will propose legislation to improve adjustment assistance programs.