The Reagan administration told Congress yesterday that it plans to sell $530 million in arms to Taiwan, about $200 million less than had been expected but still the largest such sale of the administration.

Congressional and State Department sources attributed the reduction to military officials in Taipei, who reportedly decided they did not wish to purchase all the arms that Washington was offering at this time.

The sale is certain to draw fire from the People's Republic of China, which regards Taiwan as a wayward province that should not be sold arms by the United States or other countries.

The official notice of the long-expected sale, apparently timed for late yesterday, to draw as little public attention as possible, came as Sino-American relations have been showing some signs of improvement after many months of trouble.

Among the signs of a modest upturn are an impending visit to Washington in September by Foreign Minister Wu Xuequian, negotiations on a visit to Peking this fall by Secretary of Defense Caspar W. Weinberger and progress in negotiations here earlier this week toward conclusion of a Sino-American nuclear cooperation agreement. The agreement would make it possible for U.S. firms to sell nuclear power equipment and fuel to China.

Still unresolved, however, is a hoped-for exchange of visits by Premier Zhao Ziyang and President Reagan. A visit here by Zhao is considered by the U.S. side as a necessary first step toward a Peking trip by Reagan.

Zhao has accepted a U.S. invitation in principle, but has not set a date, apparently because of the unsettled state of relations. Reagan is planning a trip to Japan, South Korea and Southeast Asia in November, but China is not on his itinerary.

A senior State Department official who briefed reporters on the nuclear cooperation talks reported progress but no agreement in three days of discussions with a team led by Jai Weiwen, China's nuclear commissioner.

The official held out the hope that after further consideration China will agree to mutual acceptable terms for a cooperation pact.

Such a pact, which would involve restrictions on Chinese use and transfer of U.S.-supplied nuclear equipment and material, would make possible as much as $10 billion in nuclear sales to China by U.S. firms, according to industry sources. Until recently there seemed little prospect of a U.S.-China nuclear cooperation agreement, because of China's adamantly independent policy in the nuclear field. However, a gradual shift in Peking's attitude has been noted.

Washington sources said China is preparing to join the International Atomic Energy Agency and to take other steps to cooperate with international norms in the atomic area.

The arms sale to Taiwan announced yesterday includes aircraft spare parts, surface-to-air and sea-launched missiles and kits for upgrading U.S. tanks previously sold to Taiwan.

The State Department said the sales are in keeping with last August's Sino-American joint communique, in which Washington promised to reduce gradually the quantity and quality of U.S. arms sales of Taiwan.

The State Department said $320 million had been sold to Taiwan earlier this year, but that all of the items in the new $530 million purchase would not actually go to Taiwan this year. Therefore, officials said, they "don't anticipate" exceeding a self-imposed ceiling of $800 million in sales to Taiwan in the current year.