U.S. officials today reported the first sign of progress in resolving the Taiwan arms sales issue, suggesting a possible thaw in Chinese-American relations following two days of high-level talks between Vice President Bush and Peking leaders.

China has yet to characterize fully the visit but agreed to a statement issued by Bush saying his talks have "greatly improved mutual understanding." Vice Premier Wan Li said at a reception tonight that the talks were "useful and enabled us to see even more clearly the importance and urgency of removing the serious obstacles" from bilateral relations.

At an earlier briefing, U.S. Ambassador Arthur Hummel indicated that the personal involvement of the vice president has given fresh momentum to stalled negotiations on U.S. arms sales to Taiwan, which have driven bilateral relations to the breaking point.

Hummel said Bush has engaged in "substantive talks," but Hummel refused to reveal whether Bush carried new proposals from Washington.

"We've made progress," said Hummel, sounding the first positive note since talks began in November. He said frozen negotiating stances of both sides have changed "in the sense that a very high-level exchange of views of this sort produces better understanding and lays the groundwork for an eventual solution."

Although Hummel's comments and the initial Chinese response represent a significant change in tone after months of pessimism, it is unclear whether Bush has truly helped facilitate a settlement.

Bush, who returns to Washington Sunday, spent 2 1/2 hours this morning meeting with China's de facto ruler, Vice Chairman Deng Xiaoping. Deng said at the outset he hopes Bush's visit will "disperse the shadows and dark clouds overhanging our relations."

China has threatened to downgrade relations with Washington and withdraw its strategic cooperation against the Soviet Union if the United States fails to set a timetable for halting arms sales to Taiwan, which Peking considers a breakaway island.

Washington says it is legally bound by a congressional act to provide weapons necessary for the defense of Taiwan, which was a U.S. ally for 30 years before Washington shifted its recognition to the Communist mainland in 1979.

Hummel said the act of Congress passed after Washington normalized relations with Peking "cannot be changed by any unilateral discussion" with Chinese officials.

"What further progress can be made remains to be discovered in the discussions that both sides have agreed will continue at other levels," said the ambassador.

The Reagan administration has asked Congress to approve $60 million in military spare parts for Taiwan. Although Taiwan's request for new advanced aircraft was rejected last year, the administration is publicly committed to continue supplies of F5E jet fighters.

Peking accepted the spare parts deal on U.S. assurances that it was sealed with Taiwan before Sino-American talks on the issue began, that no weapons are involved and that Washington will put off thought of new arms supplies to Taiwan while talks with Peking proceed.

Although the understanding has managed to finesse the issue, Chinese and foreign analysts believe the calm will last only until the White House feels obligated to sell more F5Es to Taiwan. The co-production agreement expires next year.

Bush, who headed the U.S. liaison office in Peking in the mid-1970s before full diplomatic relations were established, has tried during his stay to narrow differences on the Taiwan issue while emphasizing the larger strategic interests the two nations share in blocking Soviet advances.

China, originally a strong advocate of such a strategic partnership, has cooled to the idea as the Taiwan issue has dominated the relationship. Peking has been moving into a Third World position, poised against both superpowers.