Evidently irritated by public discussion of American arms sales to China and still uneasy about U.S. relations with Taiwan, Peking is stalling the start of the first Sino-American talks on the proposed sales that were originally scheduled to be held in Washington this month, according to informed sources.

U.S. Secretary of State Alexander M. Haig Jr. announced in June after a three-day visit here that the vice chief of China's general staff would travel to Washington in August to discuss an unprecedented U.S. offer to sell China weapons.

But the Chinese have made it clear that the vice chief of staff, Liu Huaqing, will not go to the U.S. capital this month, and although the United States has suggested that the military leader arrive in September, Peking has not yet responded, sources said.

In Washington, State Department officials said the postponement of the planned mission from its original August timetable was at the suggestion of the United States, because of the need for additional time for preparations. The postponement was made known by a senior U.S. official 10 days ago. Officials confirmed that China has not yet responded to the September dates suggested by Washington.

While China's leaders have given no explanation for the delay nor indicated when the mission might begin, they are known to have been unhappy at Haig's public announcement of plans for the Liu visit at a press conference in Peking, informed sources said.

The Chinese would have preferred that the plans be kept quiet so as not to suggest that Peking had consented to a major step forward in Sino-American relations while the volatile question of U.S. policy toward Taiwan remained unresolved, sources said.

"It's the usual bureaucratic grumbling you get when somebody talks out of turn," an informed source said in describing Chinese reaction to the Haig disclosure.

According to a source who has access to Chinese foreign policy officials, Peking may still be deciding "how far it wants to go" in developing a new military relationship with Washington while the Reagan administration remains sentimentally attached to Taiwan and unwilling thus far to rule out new weapons sales to it.

For weeks preceding the Haig trip, China had warned publicly and privately that bilateral relations faced grave danger unless the new administration gave up any idea of upgrading relations with Taiwan's Nationalist leaders or selling them the sophisticated jet fighters they are seeking.

Official displeasure caused by Haig's unexpected remarks in Peking reportedly hardened when Reagan held his own news conference in Washington four hours later and pledged to live up to the act of Congress allowing U.S. sales of defensive arms to Taiwan.

Peking has shown no sign of softening its Taiwan stand since Haig left. Indeed, the official press has pointedly reminded Washington that the very maintenance of good relations -- not to mention any type of military link -- depends on U.S. willingness to divorce itself from its old allies on Taiwan.

As another reminder of its independence from Washington and its ability to carry on without U.S. weapons, the Chinese press published a mildly toned analysis of the Sino-Soviet border dispute on the day of Haig's departure. Some diplomats here saw that as a signal to Washington that arms might not even be necessary to handle the vexing boundary issue.

China also has shifted the focus of its foreign policy more decisively toward the Third World in recent weeks, holding out the possibility of aligning with developing nations instead of the West in Peking's efforts to resist what it believes is a Soviet strategy to encircle China.

Despite these recent diplomatic moves, Peking still considers its relationship with Japan, Western Europe and the United States as the cornerstone of its foreign policy and the best way to offset growing Soviet power, according to diplomatic analysts here.

The U.S. decision announced by Haig two months ago was the latest move in what has been an increasingly close military relationship with China since former defense secretary Harold Brown visited here in January 1980 and offered the sale of technology with possible military use as well as military support equipment, such as radar equipment and trucks.

What the Reagan administration has done is remove China from the munitions control restrictions preventing any sale of lethal weapons to the Asian communist giant. But Peking's arms requests will be considered on a "case-by-case" basis after consultation with Congress and U.S. allies, according to Haig.

The trip of vice chief of staff Liu Huaqing was originally seen as an opportunity to discuss China's military needs and orient Chinese officials to the bureaucratic maze of approvals required for purchase of U.S. weapons.