The Reagan administration, declaring a strong U.S.-China relationship to be "one of the highest goals" of its foreign policy, expressed renewed hope yesterday that continuing negotiations will succeed in resolving the dispute about U.S. arms to Taiwan.

An address by Undersecretary of State Walter J. Stoessel Jr. to a China-oriented trade organization was the administration's fullest public expression of its China policy in many months. It presented new reassurance and new gestures to Peking at a delicate and possibly final stage of negotiations on the Taiwan issue.

The speech to the National Council for U.S.-China Trade also came as a new complication arose in Sino-American relations because of the arrest in Peking of an American graduate student, Lisa Wichser, on charges of participating in the theft of "state secrets." Apparently referring to the Wichser case, Stoessel said in his speech that "we vigorously intend to uphold" the consular convention between the two nations, which provides "important protections for Americans in China."

According to Stoessel, Vice President Bush's recent trip to China resulted in "good progress" on Taiwan arms sales, which he described, using the past tense, as "the one serious issue that threatened good relations."

Saying that discussions continue on "this complex, historical issue," Stoessel expressed the belief that with statesmanship, vision and good will "we will be able to overcome our difficulties." Failure to do so, he added, would be "a great misfortune" that would only benefit "our common adversaries," apparently a reference to the Soviet Union.

The personal participation of Bush and letters from President Reagan on the occasion of Bush's trip were intended to set forth U.S. views on Taiwan arms in ways that the Chinese would find unmistakably authoritative. The Chinese, in turn, are reported to have expressed their position to Bush in clearer fashion than in the past.

The basic outlines of a settlement, as described in the letters and the guarded comments of Washington sources, involve a U.S. commitment to decrease its arms supply to Taiwan in the context of progress toward a peaceful solution of the China-Taiwan problem. Peking is reported to be no longer insisting on establishment of a cutoff date for U.S. arms sales, a demand Washington has said it cannot meet.

The administration reportedly has reformulated its proposals for a settlement of the Taiwan issue in the light of Bush's trip. There is hope, but no certainty, on the part of administration officials that China will accept the reformulation and bring to an end months of tension between Washington and Peking.

Taiwanese authorities, who filed a stiff protest about being kept in the dark on the U.S. letters in connection with the Bush trip, have recently been briefed, according to the State Department. The Taiwanese are expected to express their unhappiness to Sen. Barry Goldwater (R-Ariz.), who is visiting there. At the same time, Senate Republican Leader Howard H. Baker Jr. (Tenn.) will see Chinese leaders in Peking, after having met with Reagan on the Taiwan issue.

Stoessel, in his address, announced that the administration has taken several new steps of accommodation toward China while the Taiwan arms negotiations continue. Among these are a recent White House directive reaffirming a "substantial liberalization" of U.S. export policy, and a presidential order issued last December lifting the ban on sales of munitions to Peking.

According to Stoessel, there has been "a dramatic rise" in approvals of commercial export licenses for China over the past year. China has taken no new steps in the military supply field, however, because of the unresolved dispute over arms to Taiwan.