A letter from President Reagan to Chinese Premier Zhao Ziyang this weekend commemorating the 1972 breakthrough on Sino-American relations may play a role in breaking a new political logjam between the two countries, official sources said yesterday.

The letter, commemorating the 10th anniversary of the Shanghai Communique, was dispatched at a time of growing optimism in Washington that a way can be found to resolve new difficulties over the issue of U.S. arms sales to Taiwan.

Among other things, the letter is believed to reiterate the broad principles of Sino-American relations along lines acceptable to the Chinese.

Several recent diplomatic exchanges through the U.S. Embassy and Chinese Foreign Ministry in Peking are reported to have diminished some of the barriers to a negotiated accommodation in the dispute, which has emotional and political overtones in both countries.

The current problems of Sino-American relations seem to be working out, Sen. Charles H. Percy (R-Ill.), chairman of the Senate Foreign Relations Committee, reportedly told a group of China experts here earlier this week.

Administration sources, while cautioning that crucial answers from the Chinese side have not yet been received, did not dispute reports that the chances for success in the current negotiations seem to have improved.

The discussions began in Peking the weekend of Jan. 9-10 during a visit by Assistant Secretary of State John H. Holdridge to acquaint the Chinese with Reagan's decisions to continue U.S. sales to Taiwan of weapons already in the island bastion's inventory but to deny sale of a more sophisticated fighter plane, the FX.

The Chinese strongly objected as a matter of principle to the continued U.S. military supply to Taiwan, which it considers a wayward province. Holdridge was reportedly subjected to tough demands in Peking, including an insistence that the United States set a definite date for termination of all military sales to Taiwan.

Public and private statements from the Chinese side suggest that the demand for a definite termination date has been dropped. Instead, the two sides are believed to be working on language recognizing Chinese sovereignty over Taiwan and tying future arms sales to developments between Peking and Taipei.

Such formulas for the future were suggested to Reagan by Secretary of State Alexander M. Haig Jr. in a memorandum on the Taiwan arms issue last November, according to an account by Tad Szulc in the Los Angeles Times.

Haig's memo, as reported by Szulc, suggested that the United States could agree to keep its arms flows to Taiwan below the "unusually high" level of the last year of the Carter administration "so long as Peking pursues a peaceful Taiwan policy."

Haig was also reported to have said, "While we cannot specify a time certain for ending arms sales, we can develop formulation linking our future action to genuine progress on peaceful reunification."

The Shanghai Communique was signed by President Nixon and Premier Chou En-lai on Feb. 27, 1972, at the conclusion of Nixon's epochal trip to China.

In this document, the United States acknowledged that "all Chinese on either side of the Taiwan Strait maintain there is but one China and that Taiwan is a part of China." The United States also agreed in the document to withdraw its military forces and installations from Taiwan "as the tension in the area diminishes."

President Carter went beyond the Shanghai Communique in establishing full diplomatic relations with Peking on Dec. 15, 1978, when the United States recognized the People's Republic of China as "the sole legal government of China."

Chinese negotiators in the current round reportedly had hoped that agreement between the two sides on future U.S. sales to Taiwan could be completed in time for a joint announcement this weekend, on the Shanghai Communique anniversary. There was no sign yesterday that this target could be met.