“It was red carpet like nobody, I think, has probably ever received,” the president added.
By some measures, he was right. Mr. Trump made no major gaffes. The closest he came was calling the North Korean leader Kim Jong-un “short and fat” in a tweet. He also faced criticism for failing to challenge the Philippine president, Rodrigo Duterte, who is accused of ordering thousands of extrajudicial killings, on human rights.
But Mr. Trump’s energy did not flag and he was accorded a lavish reception at every stop, especially Beijing, where President Xi Jinping threw open the doors of the Forbidden City.
“Like any Trump endeavor, there were the inevitable distractions with tweets about the physical appearance of leaders and clear signals that he prefers the company of tyrants like Putin and Duterte,” said Kurt M. Campbell, a former assistant secretary of state for East Asian affairs.
Still, Mr. Campbell said, “If this trip were a high-wire act, President Trump managed to get to the other side.”
And yet there were subtler signs of tension, which spoke to the conflicting messages Mr. Trump brought to Asia and suggested a level of disarray in the White House’s policy toward the region.
Before his meeting with Prime Minister Shinzo Abe of Japan and Prime Minister Malcolm Turnbull of Australia, for example, Mr. Trump had a brief contretemps with Mr. Turnbull over trade imbalances after he asserted that the United States ran deficits with “almost everybody.”
“Except us,” Mr. Turnbull interjected.
Mr. Trump made trade a major part of his message in Asia, and his tone grew more bluntly nationalistic as the trip wore on. After declaring in Beijing that he did not blame the Chinese for chronic imbalances with the United States, he delivered a withering denunciation in Vietnam of regional trade pacts, like the Trans-Pacific Partnership, from which Mr. Trump has withdrawn the United States.
The president delivered that message in a speech that was supposed to explain his concept of a “free and open Indo-Pacific” region. The idea, which Trump officials borrowed from the Japanese, is that the region’s four major maritime democracies — the United States, Japan, Australia and India — will constitute a bulwark against a rising China.
But this theme was largely lost in the jeremiad on trade. Critics said it testified to the stubborn divide within the administration between mainstream foreign policy figures like Matthew Pottinger, the senior director for Asia at the National Security Council, and economic nationalists like the policy adviser Stephen Miller, who took a strong hand in writing the speech.
“The Indo-Pacific framing is clearly the handiwork of his more experienced and internationally-minded senior national security team, while the ‘America First’ theme of demanding zero-sum concessions from all our trading partners is not,” said Michael J. Green, senior vice president for Asia at the Center for Strategic and International Studies.
Mr. Trump’s invitation for one-on-one trade negotiations with the United States, Mr. Green said, was likely to fall on deaf ears in Asian countries, many of which went though fierce debates before signing on to the Pacific trade deal and now want to reap its benefits.
“That’s like a sheriff squaring up for a showdown with the town outlaw by announcing to the posse that he wants a gunfight with each of them at the same time,” said Mr. Green, who served as President George W. Bush’s senior adviser on Asia policy.
Indeed, while Mr. Trump was preaching his go-it-alone economic message, the 11 countries still in the Trans-Pacific Partnership made significant progress toward finalizing the agreement without the United States. They have given it an even wordier new name, the Comprehensive and Progressive Agreement for Trans-Pacific Partnership.
“I think this will be a strong message for not only Asia, but also other regions in the world,” Japan’s economy minister, Toshimitsu Motegi, told reporters.
Mr. Trump’s mixed messages applied to China, too. In Beijing, he embraced the Chinese leader unlike any American president going back to Richard M. Nixon. He said nothing publicly about China’s human rights record. And he cast Mr. Xi as a popular leader who could solve the nuclear crisis with North Korea.
“He’s a strong person,” Mr. Trump said to reporters. “He’s a very smart person. I like him a lot; he likes me. But, you know, we represent two very different countries. But we get along very well. And that’s a good thing that we get along; that’s not a bad thing.”
White House officials said Mr. Trump’s charm offensive had paid off in extracting new commitments from China to shut down North Korean bank accounts. But officials acknowledged that China had not budged on their No. 1 request on North Korea: to cut off all shipments of oil to the North.
Nor did it announce major moves to open its markets during Mr. Trump’s visit, in part because the president did not ask for any.
Moreover, Mr. Trump soft-pedaled his call for China not to colonize the South China Sea. While he emphasized the need for free navigation and open shipping lanes during his visits to Vietnam and the Philippines, he did not single out China, which has clashed with those neighbors as it has built military installations in the disputed waterway.
One of Mr. Trump’s aides marveled at the sheer size of China’s claims in the South China Sea, noting that Air Force One flew for three hours over these contested waters on its way from Hanoi to Manila.
During his meeting with Vietnam’s president, Tran Dai Quang, Mr. Trump offered his deal-making skills to mediate disputes in the South China Sea. But some Asian countries are no longer as ready to pick fights with China. Mr. Duterte stopped construction last week on a sandbar in disputed waters, as part of a broader effort to draw closer to Beijing.
Just before leaving Manila on Tuesday, Mr. Trump told reporters he had repaired what he claimed had been a “horrible” relationship between Mr. Duterte and the United States. “We have a very good relationship,” he said. “I would actually say, probably better than ever before.”
After 12 hectic days in Asia, even Mr. Trump’s critics acknowledge he projected an air of engagement. The question, they said, is whether his mixed messages will open the door further for China’s incursions in the region.
“Despite all the craziness of Trump, the U.S. remains in the game in Asia,” said Evan S. Medeiros, a former adviser to President Barack Obama on China. “But the U.S. is no longer driving the agenda.”