The two leaders met for the first time briefly on Friday at an economic summit in Danang, Vietnam, and were photographed raising wine glasses together in a toast at the opening dinner of the Association of Southeast Asian Nations forum on Sunday. Images of them appearing at ease with one another and, like other leaders at the summit, wearing traditional Barong Tagalog shirts were published in Philippine newspapers.
On two occasions, however, Trump declined to answer shouted questions from reporters about whether he had pressed Duterte on human rights.
"We've had a great relationship," Trump told reporters, sitting with Duterte at the start of the bilateral meeting. "This has been very successful." He praised Duterte's handling of the summit and said, "I've really enjoyed being here."
As Trump pivoted to talking about the nice weather in Manila, Duterte cut off the American reporters who tried to press Trump on human rights.
"Whoa, whoa," he protested. "This is not a press statement. This is the bilateral meeting."
Duterte at one point called reporters "spies," prompting Trump to chuckle. "You are," Duterte repeated.
A spokesman for Duterte said after the meeting that human rights did not come up, although the Philippine leader did raise his efforts in the "drug menace."
White House press secretary Sarah Huckabee Sanders told American reporters that the two leaders spoke about combating terrorism and illegal drugs, as well as bilateral trade. Human rights, she said, came up briefly in the context of the Philippines' drug war. She did not elaborate.
Ahead of his visit here, Trump boasted that he expected things to go a lot better than during the last trip to the Philippines by President Barack Obama. However, Trump appeared to mix up his references. Obama canceled a bilateral meeting with Duterte in September 2016 after the Philippine leader made derogatory comments about him and the United States, a longtime treaty ally. Obama's 2015 visit to Manila went smoothly — before Duterte was elected.
"I have a sense that he is not going to address human rights, largely because he is trying to build a relationship with Duterte. This 10-day trip is about building alliances in response to North Korea," said James Zarsadiaz, director of the Yuchengco Philippine Studies program at the University of San Francisco.
White House aides said Trump routinely brings up human rights in his private conversations with world leaders, and in a couple of notable instances he has addressed the matter in public on his five-nation Asia trip. In a speech to the South Korean parliament, Trump called North Korea "a hell no person deserves," and he laid out in sometimes gruesome detail the abuses Pyongyang has perpetrated — including purportedly killing babies and carting the bodies away in buckets.
In Tokyo, Trump met with the families of Japanese citizens who were abducted by North Korean agents four decades earlier. Other presidents, including Obama and George W. Bush, also met with the families.
"We'll work together and see if we can do something, now the spotlight is on," Trump said at a news conference with Prime Minister Shinzo Abe, calling the abductions a "very, very sad thing."
Yet Trump has not talked about human rights more broadly outside the context of North Korea. He has yet to make any public statement in the two months since Burma escalated a military campaign against the Rohingya, a Muslim ethnic minority that has been persecuted for years by the country's Buddhist majority. The United Nations' top human rights official has called the military campaign "a textbook example of ethnic cleansing."
In Vietnam, Trump embraced the communist nation's leaders, paying a state visit to Hanoi, without publicly raising an ongoing crackdown on political speech and independent journalists. Obama also embraced Hanoi, but his administration insisted on the release of hundreds of political prisoners and had sought to use a 12-nation trade deal, the Trans-Pacific Partnership, to enact new protections for workers in Vietnam and elsewhere. Trump, on his third day in office, removed the United States from that deal.
On Thursday, as Trump flew from China to Vietnam, a White House official told reporters aboard Air Force One that Trump has been "quite concerned" about Burma.
"It's come up in a number of his conversations with Southeast Asian leaders, and certainly he'll be discussing it, and publicly as well," said the official, who was not authorized to speak on the record. As of Monday afternoon, Trump had yet so do so.
The question of whether Trump will press Duterte on human rights is often talked about as a test of U.S. power, both in the Philippines and in the region as a whole.
Although the Obama administration promised a "pivot" to Asia, in part structured on human rights and U.S. values diplomacy, there has long been a sense that U.S. influence in the Asia-Pacific region is waning while China's is on the rise.
Over the last decade, China has stepped up trade, investment and tourism in Southeast Asia, becoming a major economic player with close ties to the political and military elite.
All 10 ASEAN member states joined the Asian Infrastructure Investment Bank, a Chinese-led multilateral financial institution that is issuing billions in loans. An authoritarian state that sharply curtails free speech and political dissent, China has not tied human rights reforms or worker protections to its economic largesse.
The Obama administration sought to unite ASEAN members around values that include human rights. But the 10 member countries have widely disparate political systems — some democratic, some authoritarian — and economic systems.
Trump aides, including Secretary of State Rex Tillerson, said the president believes it is more effective to discuss such human rights issues in private; Trump has helped gain the release of a number of Americans who had been detained in Asia and the Middle East. The president railed about North Korea's mistreatment of American college student Otto Warmbier, who died shortly after being released from 17 months of captivity.
Across both East and Southeast Asia, U.S. allies are uncertain about what Trump stands for and nervous about what he does next, said Richard Heydarian, a security analyst and author of "The Rise of Duterte."
"They see a total collapse of American soft power, largely because of Trump, and also American structural decline, especially relative to China," he said. But it's a mistake to see this as a clear win for the Chinese, he added. Despite China's spending in Southeast Asia, countries are not ready to align with Beijing, which is seen as a bully over its military-led maritime expansion in the South China Sea and its economic pressure.
Absent a clear leader in the region, middle-power countries, including Japan, Australia and India, are stepping up their own diplomacy. Trump was scheduled to meet with leaders from each of those countries on Monday amid talk that they would form a "quad" of powers to help hedge against China in the Indo-Pacific.
Duterte made his frustration with the United States clear, lashing out at Obama for criticizing the anti-drug campaign and threatening to curtail U.S.-Philippine military ties.
He announced that he wanted a divorce from the United States and planned to align himself with China's "ideological flow." China, in turn, promised money for major infrastructure projects and military upgrades.
But despite protests against Trump in Manila during his visit, a majority of Filipinos are more comfortable with the United States than with China and are certainly not prepared to cast their lot with Beijing alone.
Duterte's administration has continued to work with the United States on a range of issues and still takes money for counternarcotics work, police training and other things. In the run-up to Trump's visit, Duterte struck an almost conciliatory tone.
The upshot is that U.S. influence in the Philippines is not over, and Trump probably has the political capital to nudge Duterte on the drug war, should he choose to do so, experts said.
"The credibility of the U.S. is at stake because of Trump's unsophisticated ways in diplomacy," said Zarsadiaz, the Philippine studies director. "In the grand scheme of things, in Asia, there is still this sense that the U.S. is an arbiter of justice. . . . Time will tell whether Trump will follow the lead of congressional leaders, of the U.N., of Amnesty International, and stand behind what are seen as American principles."