China and the United States, whose relations already are seriously strained, may be headed for another skirmish over plans by Pan American Airways to reopen its air link with Taiwan in June, according to diplomatic sources here.

China has heatedly protested the move by Pan Am, which is the only U.S. carrier serving the Chinese mainland. The Chinese protests are seen by informed sources as a veiled threat of retaliations that could disrupt Chinese-U.S. air traffic.

Peking, however, is likely to stop short of any action that might seriously impair its burgeoning economic ties with the United States, the sources said.

The Chinese objections follow a recent Reagan administration decision to grant Pan Am permission for three flights a week to Taipei, the capital of the rival Chinese government on Taiwan. Pan Am gave up that route in 1979 to serve what then appeared to be a potentially more lucrative link with Peking.

The financially troubled U.S. carrier is believed to be operating the Peking route, which it opened in 1981, at below capacity and reportedly has said it would reactivate its service to Taiwan for purely "economic" reasons.

Western diplomats, who declined to be identified, said the dispute "is one of the dark clouds hanging over the relationship" between Peking and Washington. It comes at a time when ties have been badly frayed over American arms sales to Taiwan, a series of trade wrangles and political defections to the United States.

A Chinese move to suspend Pan Am's landing rights in Peking, sources said, "would throw the U.S.-China civil air agreement into the dirt." Under the 1980 air pact, the United States would almost certainly retaliate by revoking reciprocal privileges in the United States for the Civil Aeronautics Administration of China, China's state-run airline.

But no one here thinks that Peking wants to let things go that far, at least for the moment. At stake are China's trade and economic ties with the United States, which are important to the country's ambitious plans for economic development. A serious falling out in bilateral air transport agreements would complicate business travel to and from China and hamper Peking's bid to earn foreign currency by promoting foreign tourism here.

Diplomatic analysts here speculate that China might take a series of "intermediate steps" to symbolize its displeasure, including a slowdown in local crews' ground service, refueling and luggage handling for Pan Am flights.

Tensions between the two countries have been worsened by Peking's severing of all official cultural and athletic ties with the United States for 1983 following the Reagan administration's decision earlier this month to grant political asylum to Chinese tennis star Hu Na.

While the granting of asylum touched off a stream of anti-American rhetoric in the state-controlled media here, Chinese authorities appear to have taken pains to signal that economic ties would not be seriously affected. Last Monday, for example, China's top leader, Deng Xiaoping, reportedly told a group of visiting American businessmen that his country's "open door" economic policies would remain in effect.

Although "the Chinese seem to be going out of their way to keep up momentum in the business relationship" with the United States, a western trade analyst said, they are taking the Pan Am affair "very seriously." Chinese authorities have not openly threatened to suspend Pan Am service to Peking but have strongly hinted in a letter to the U.S. Civil Aeronautics Board that future "smooth operations" of Chinese-U.S. air transport agreements might be at risk, informed sources said.

"Matters of face and principle are very important here," a source said. "Even if the Chinese would be shooting themselves in the foot, they may feel obliged" to retaliate for Pan Am's reopening of the Taiwan route.

For the Chinese, the issue raises broad questions of what the leadership here commonly refers to as China's sovereignty and national dignity. China claims that Taiwan is part of Chinese territory, something that Peking believes gives it the right to impose conditions on Washington-Taipei relations.

To U.S. officials, the matter comes under what they consider legally binding arrangements set out in a variety of trade agreements between the two countries, in which China has acknowledged the right of the United States to maintain "unofficial" cultural and commercial ties with Taiwan. Officials also argue that the United States has the right to open new air routes under a web of independently negotiated civil aviation agreements with China, Taiwan and Japan.

Another potential loser in any serious quarrel over aviation rights between Washington and Peking is Northwest Orient Airlines, which has recently gained White House approval to start air cargo service to Peking, Shanghai and Canton.

Although Northwest has for years operated an air link between Tokyo and Taipei, Peking has not so far raised public objections to the deal, which is provided for under the existing U.S.-Chinese aviation pact, diplomatic sources here said.