Peking — A cordial exchange of messages between President Reagan and Prime Minister Zhao Ziyang signals that China and the United States are making strenuous efforts to resolve their differences over US arms sales to Taiwan.
Neither Mr. Reagan nor Mr. Zhao mentioned Taiwan or the Soviet Union in his letter marking the tenth anniversary of the Shanghai Communique, which opened the way to normalization of Sino-American diplomatic relations three years ago and to the flowering of contacts in ever-widening fields since then.
But their letters are the warmest comments on the state of relations between Peking and Washington to be made in the months since the arms sales dispute began. They offer hope that the threatened downgrading of official relations between the two countries can be avoided and that the broadening and deepening of Sino-American ties can be resumed.
Mr. Zhao's letter was more reserved than Mr. Reagan's, since China is the one demanding limits to the arms sales.
But it expressed the premier's belief that Sino-American relations will continue to develop as long as both governments adhere to the principles established in the Shanghai Communique and the joint communique of Jan. 1, 1979. The letter also promised that China is willing to work with the US toward better relations.
President Reagan in his letter expressed a desire to build a stronger bilateral and strategic framework for long-term friendship between the two nations. He reaffirmed ''the positions agreed to in the Shanghai Communique and the joint communique on the establishment of diplomatic relations,'' and expressed his willingness ''to work with our counterparts in Beijing to overcome differences and deepen United State's China ties.''
The key phrase in the two documents referred to by both parties is in the joint communique of Jan. 1, 1979: The US recognized ''the government of the People's Republic of China as the sole legal government of China.''
''Within this context,'' it continued, ''the people of the United States will maintain cultural, commercial, and other unofficial relations with the people of Taiwan.''
The joint communique also stated: ''The government of the United States of America acknowledges the Chinese position that there is but one China and Taiwan is part of China.''
The Shanghai Communique did not go this far, but it did acknowledge the principle of one China and of Taiwan as part of that China.
Mr. Reagan's willingness to reaffirm the two communiques suggests not only a backing away from the rhetoric of his 1980 campaign but also a recognition of the importance of the Sino-American strategic relationship.