From Tokyo to Beijing, Mr. Trump has played the dealmaker with foreign leaders, flattering them personally even as his administration pushes hard-edge views on economic issues.
But over time, several experts said, this balancing act may be impossible to maintain. Already with China, Mr. Trump has had to soft-pedal his aggressive trade agenda in an uphill effort to persuade President Xi Jinping to do more to press the neighboring North Korean government.
With the smaller nations of Southeast Asia, Mr. Trump may feel less pressure to compromise. His comments in Vietnam lacked the solicitous tone he had used in China and Japan, veering into the defiant populism he used on the campaign trail. Yet his go-it-alone message could drive these countries further into the orbit of China, which has moved at this meeting of Pacific leaders to fill the vacuum left by the United States.
“The region is looking for a robust American presence, not just on security but on trade,” said John Delury, an associate professor of Chinese studies at Yonsei University in Seoul, the South Korean capital. “For Trump to come with an ‘America First’ agenda leaves Asian leaders in the lurch.”
Jeffrey A. Bader, a former China adviser to President Barack Obama, said Mr. Trump’s words would make Asian leaders “feel that the U.S. is less of a factor in the region.”
“They’re always looking for hedges against local bullies, like China,” he added, “and the U.S. is much less of a hedge.”
Indeed, Mr. Trump was the odd man out at this meeting of the Asia-Pacific Economic Cooperation forum. The other 20 leaders formally endorsed the idea of a liberal trade regime, arbitrated by the World Trade Organization, and condemned moves to erect new barriers.
“We recognize the work of the W.T.O. in ensuring international trade is rules based, free, open, fair, transparent, predictable and inclusive,” the members wrote in their joint statement released on Saturday, using language that American negotiators had reportedly resisted.
On Friday, Mr. Trump railed against the W.T.O., accusing it of treating the United States unfairly. Rather than uphold principles of free trade, he said, it contributed to a systematic exploitation of Americans, in which “jobs, factories and industries were stripped out of the United States.”
As the Asian leaders gathered here on Saturday, much of the attention focused on whether Mr. Trump would meet with President Vladimir V. Putin of Russia.
The White House steered clear of a formal meeting, though the two men conferred briefly. The United States and Russia later issued a joint statement on Syria that reaffirmed previous commitments to defeat the Islamic State and to untangle conflicts between their respective forces on the Syrian battlefield.
Still, for Mr. Trump, this trip has been a surprisingly disciplined exercise. Mr. Trump joined the other leaders in wearing matching electric-blue, traditional Vietnamese shirts at dinner on Friday evening, adhering to a peculiar tradition of this summit meeting.
With a jam-packed schedule, he has tweeted sparingly and has kept generally on message. The White House has cut down on unscripted moments, limiting media access and acquiescing to the Chinese reluctance to allow questions after his joint statements with Mr. Xi.
Mr. Trump’s encounters with leaders have been harmonious — even leaders, like President Moon Jae-in of South Korea, with whom he has differences. That is in keeping with Mr. Trump’s pattern throughout his presidency, though it was perhaps never as striking as in Beijing, where he lavished praise on Mr. Xi, only to criticize China’s trade practices a day later in Vietnam.
“There is some value in treating counterparties with respect, in trying to build relationships with them, despite the distasteful nature if it,” said Mr. Bader, the former Obama official.
But if Mr. Trump’s stops in Northeast Asia were aimed at building a coalition against North Korea, his swing through Southeast Asia seemed calculated to remind people that he has little use for the post-World War II concept of the United States as global leader.
At moments, his speech in Vietnam had the tub-thumping atmosphere of one he may have given in Pennsylvania or Wisconsin. When a member of the audience broke into applause after he accused countries of not opening their markets to American goods, a sardonic Mr. Trump exclaimed: “Funny. They must have been one of the beneficiaries.”
Administration officials framed the speech as a chance for Mr. Trump to promote a “free and open Indo-Pacific,” which the White House has embraced as its answer to Mr. Obama’s “Asia pivot.” But the president put little meat on the bones, emphasizing the sovereignty and independence of nations over common interests or universal rights.
“Human rights are, in essence, an international agreement,” said John Sifton, the director of Asia advocacy for Human Rights Watch. “When he talks about trade in those terms, it suggests that he doesn’t hold the multilateral legal system in very high regard — and that’s frightening.”
Human rights groups, Mr. Sifton said, were focusing their energies on lobbying Canada and Japan rather than the United States.
Chinese leaders do not dwell on human rights either, to say the least. But Mr. Xi came to Vietnam primed to take over some of the ground usually commanded by the American president. During his speech, which came right after Mr. Trump’s, he declared, “Opening up will bring progress, and those who close down will inevitably lag behind.”
In the absence of an alternative sales pitch from the United States, experts said, China will inevitably make further gains.
“China has made significant inroads in cultivating Southeast Asia,” said Tang Siew Mun, head of the Asean studies center at the ISEAS-Yusof Ishak Institute in Singapore. “This isn’t an entirely bad proposition for the region, but China’s success is disastrous for the U.S., as Chinese advances are at the U.S.’s expense.”
“At the end of the day,” Mr. Tang said, “‘America First’ may devolve into the U.S. being home alone.”