President Carter and Japanese Prime Minister Takeo Fukuda ended two days of talks yesterday with no agreement on the increasingly touchy question of Japan's plan to "reprocess" U.S.-supplied nuclear fuel.

Japan's $200 million reprocessing plant, which is scheduled to begin operating tests this summer, was a principal subject of the final head-to-head meeting of the two leaders in the Oval Office as well as a larger, Cabinet room session which also involved the senior diplomats of the two nations.

Carter told Fukuda that the United States will announce, in connection with the new energy policy scheduled for unveiling April 20, a general U.S. position on nuclear reprocessing. This operation, intended to make nuclear fuel reusable after an initial atomic reactions, produces weapons-grade material as one of its products.

According to Japanese reports of Carter's remarks, he strongly suggested - if he did not flatly state - his opposition to reprocessing for commercial purposes. Carter asked Japan to give close study to a Ford Foundation-sponsored report, which was presented to Carter Monday, stating that reprocessing involves few economic advantages but "the most severe risks" of atomic weapons proliferation.

Fukuda told Carter and repeated to a National Press Club audience that Japan's leadership had given a major commitment to its legislature and public that peaceful uses of atomic energy, including reprocessing, will be vigorously pursued.

The prime minister argued that Japan, as the only nation to suffer atomic bombing and one with a passionate opposition to atomic weapons, is in a "special situation" that reduces the international dangers of a reprocessing operation. By the terms of the sale, U.S. permission is required for the reprocessing of American-supplied nuclear fuel.

Carter and Fukuda agreed to bilateral consultations between senior officials in an attempt to work out an accommodation on the nuclear question before the April 20 deadline. They also agreed to future discussions about Japanese exports of colour television sets in an effort to head off a sharp U.S. tarriff increase.

Concerning Carter's plan to withdraw U.S. ground forces from South Korea, a joint communique said Carter and Fukuda "noted the continuing importance of the maintenance of peace and stability on the Korean Peninsula for the security of Japan and East Asia as a whole." The document also quoted Carter as saying that U.S. troops would be taken out in "ways which would not endanger peace" in Korea and that "the U.S. remains committed to the defense of the Republic of Korea."

A 1969 joint communique of President Nixon and Japanese Prime Minister Eisaku Sato quoted Sato as saying that the security of South Korea is "essential to Japan's own security." A 1975 communique of President Ford and Prime Minister Takeo Miki said South Korean security is "essential" for peace on the Korean peninsula, which in turn is "necessary" for peace and security in Japan and the rest of East Asia.

U.S. and Japanese officials said they placed no significance in the change of language about Korean security from being "essential" to being "important."