At the same time, the Chinese leadership will view statements by Mr. Trump with even greater skepticism. “Even though Trump has said he will support the ‘One China’ policy, China cannot fully trust him,” said Yan Xuetong, dean of the school of international relations at Tsinghua University in Beijing. “Even his own people don’t trust him,”

China’s official reaction to the telephone call, in which Mr. Trump affirmed that America would abide by the decades-old policy, was polite, even upbeat.

“The conversation was very cordial,” Lu Kang, the spokesman for the Chinese Ministry of Foreign Affairs, said at a regular news briefing on Friday. “The One China principle is the political foundation of China-U.S. relations.”

Under that policy, the United States recognized a single Chinese government in Beijing, and severed diplomatic ties with Taiwan.

American strategic leadership was damaged by Mr. Trump staking out a position and then stepping back, said Hugh White, a professor of strategic studies at the Australian National University and the author of “The China Choice,” a book that argues that the United States should share power in the Pacific region with China.

“The Chinese will see him as weak,” Mr. White said of Mr. Trump. “He has reinforced the impression in Beijing that Trump is not serious about managing the U.S.-China relationship, and preserving U.S. leadership in Asia.”

Mr. Shi said the Chinese leadership had devised a strategy to remain firm and patient with Mr. Trump, and that approach had paid off.

Even though many other world leaders had spoken to the new American president by phone since his inauguration on Jan. 20, Mr. Xi had refused to talk to Mr. Trump until he was sure that the American president would give what turned out to be a concession — an affirmation of the One China policy, Mr. Shi said.

Mr. Trump put himself in a corner by questioning the status of Taiwan, an issue that the Chinese have regarded as nonnegotiable since President Jimmy Carter implemented the One China policy in 1979, Mr. Shi added.

Some Chinese said Mr. Trump’s decision to walk back on the issue of Taiwan at least lowered the risk of conflict.

“If he agreed to the One China policy, that means there is no danger of direct war between China and the United States,” said Mr. Yan of Tsinghua University. “That fact is very positive.”

A magazine on sale in Beijing this week showed President Xi Jinping of China and President Trump. One analyst said China’s leadership had devised a strategy to remain firm and patient with Mr. Trump, and that approach had paid off.

Andy Wong/Associated Press

When Mr. Trump took a precedent-shattering phone call from President Tsai Ing-wen of Taiwan in early December, and said a few days later that he wanted to extract concessions from Beijing in return for keeping the One China policy, the Chinese government issued “ugly” statements saying it would not waver on the issue of Taiwan, Mr. Shi said.

Those statements came from the Ministry of Foreign Affairs, which said “it was out of the question” to negotiate and that the One China policy was “a core issue” that involved China’s sovereignty and territorial integrity.

In diplomatic parlance, that meant Taiwan was a rock-bottom issue China was prepared to fight over.

The tough statements were intended to recall the incident in 1995 when China tested missiles near Taiwan, prompting President Bill Clinton to dispatch an aircraft carrier through the Taiwan Strait near China’s coast.

China is militarily far stronger today, armed with far more advanced missiles and a more robust navy that includes one aircraft carrier, with more on the way.

The Chinese also decided to flatter Mr. Trump, Mr. Shi said. When the Trump administration started to make small steps to pave the way for the phone call with Mr. Xi, China was almost excessive in its response, a way of trying to reassure Washington without paying any price, Mr. Shi added.

So after Mr. Trump sent a letter to the Chinese Embassy in Washington this week wishing the Chinese people a “prosperous Year of the Rooster,” Beijing responded that it was “very happy” to receive the president’s greetings.

The American secretary of state, Rex W. Tillerson, who had pledged to uphold the One China policy during his confirmation hearings, was at the White House on Thursday before the call, apparently pointing out the risks of Mr. Trump’s approach.

“The cost to the U.S. of refusing to recommit to the One China policy was very high and Trump was persuaded,” said Bonnie S. Glaser, director of the China Power Project at the Center for Strategic and International Studies in Washington.

In an unusual move, the state-run Chinese news agency Xinhua posted on Twitter a cheeky quiz on the possible reason Mr. Trump had changed his mind on the One China policy. Twitter is banned in China.

Xinhua gave four choices, giving prominent play to the options “blackmailing didn’t work” and “China’s unyielding stance,” and including the possibility that a visit by Ivanka Trump and her 5-year-old daughter, Arabella, to the Chinese Embassy’s New Year reception last week played a role.

The tension between Washington and Beijing over Mr. Trump’s attitude to Taiwan has reverberated around the Asia-Pacific region, where American allies have worried since the December phone call with Ms. Tsai that, in the extreme, there could be armed conflict over Taiwan.

On Friday, the United States Pacific Command said that a Chinese aircraft and an American Navy patrol plane had an “unsafe” encounter over the South China Sea, The Associated Press reported. A spokesman said that the “interaction” between a Chinese KJ-200 early warning aircraft and a Navy P-3C plane took place on Wednesday in international airspace. The spokesman did not say what was unsafe about the encounter.

That Mr. Trump appears to have smoothed things out for the moment has brought relief, but does not assuage concerns about future dealings between Mr. Xi and the American president.

Both the White House and the Chinese foreign ministry said that the two leaders wanted to strengthen cooperation. The White House statement said Beijing wanted to work with Washington on a number of issues, including trade.

Mr. Trump has threatened a trade war by repeating threats of steep tariffs in response to what he portrays as China’s predatory trade practices.

Neither side specified in their statements how they would cooperate, and doubts remained in the Asia-Pacific region about Mr. Trump’s intentions on a host of issues. China values predictability, and one phone call could not deliver that, analysts said.

“Trump isn’t attached to any particular policy line with China or anyone else,” said Peter Jennings, executive director of the Australian Strategic Policy Institute. “So ‘working together’ could also be dumped whenever it suits.”

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