Vice President Bush said today that the Reagan administration is confident that China will not downgrade relations with the United States, which have been badly strained by U.S. plans to sell Taiwan $60 million worth of military spare parts. He left open the possibility that he may visit China at the end of his scheduled five-nation Asian tour.

While ostensibly here to confer with Japanese leaders on the sensitive issues of trade and defense, which have complicated the mostly friendly ties between the United States and Japan, Bush took the opportunity to stress the importance of improving Sino-American relations.

In a speech at the foreign correspondents' club here on the first leg of his nine-day tour, Bush said the United States was "absolutely resolved to strengthen our relationship with the People's Republic." He told reporters that the relationship "will prosper because it is fundamental" to the national interests of both countries and Asia as a whole.

Bush said the Chinese were "in the process of fully understanding" the U.S. position on the spare parts deal. Peking has charged that the sale infringes on China's sovereignty since it asserts that Taiwan belongs to the Chinese mainland. The sale will pass automatically in mid-May unless Congress blocks it.

Asked to comment on U.S. press reports that he might go to China, the vice president said he could not confirm the trip. He added, "If a visit . . . would be productive and useful, we could change plans, go the extra mile." He stressed, however, that "the relationship is not in such a shape to require a visit . . . to patch things up."

In an apparent bid to ease the thorny trade ties between the United States and Japan, which have resulted from Japan's booming trade surpluses, Bush said that the two countries "cannot allow trade disagreements to dominate our dialogue."

He suggested that the two sides were moving toward agreement on key trade issues, but he acknowledged that the Reagan administration was concerned about rising protectionist sentiment in the United States.

The conciliatory tone of Bush's remarks were in sharp contrast to those of senior American trade officials who have visited here in recent months to press Japan to quickly open its market to more U.S. products or face the adoption by Congress of protectionist legislation designed to enforce greater access here for U.S. businessmen.

Bush's arrival here Friday coincided with one of the largest and most vocal demonstrations in recent years by Japanese farmers, who called for Prime Minister Zenko Suzuki's government to reject strong American demands for the elimination of 22 quota restrictions Tokyo enforces on farm product imports including beef and citrus fruit and juices.

According to Japanese officials, rising resistance to U.S. trade demands has amplified the difficulties for the Suzuki government in putting together the package of "dramatic" surplus-reducing measures U.S. officials say they want Tokyo to take before the June economic summit in Paris.

According to Japanese press reports, Bush told Suzuki today that the United States had no intention of selling sophisticated warplanes to Taiwan. Bush made the remark after Suzuki suggested that a deterioration in U.S.-Chinese relations could help undermine stability in Asia.

At a press conference later in the day, however, Bush indicated that the United States would abide by a previous commitment to supply defensive military weapons to Taiwan.

Bush is due to arrive in South Korea Sunday before traveling on to other scheduled stops in Singapore, Australia and New Zealand.