“These two are talking as friends,” said Ramon Casiple, the executive director of the Institute for Political and Electoral Reform, a nonprofit promoting democracy in the Philippines. “I don’t see any reasons when they meet face-to-face that there will be any big problems.”
But the longer-term game for Mr. Duterte has been his determination to court China. Since his election, he has backed down from contentious territorial disputes with Beijing — last week, he halted a construction project in the South China Sea that brought Chinese complaints — despite an international ruling early in his presidency that backed the Philippines.
Harry Roque, a spokesman for Mr. Duterte, described his policy as a deliberate turn toward closer relationships with countries in Asia, and with China in particular.
Mr. Duterte hopes his strategy will bring billions of dollars in investment from China, though the money has been slow in coming, said Richard Javad Heydarian, an assistant professor of political science at De La Salle University in Manila.
Still, the United States and its former colony are treaty allies with a long history of cooperation. And it is clear that Mr. Duterte’s and Mr. Trump’s styles seem to mesh more than clash.
Mr. Trump set the stage for improved relations when he called Mr. Duterte in April and congratulated him for doing an “unbelievable job on the drug problem.” The United States also provided valuable military assistance — including drones and intelligence — that proved instrumental in defeating Islamic extremists during a five-month siege of Marawi City, which ended last month.
On Sunday, Mr. Trump offered to help mediate the disputes in the South China Sea, which have also pit China against Vietnam and other countries in the region. “I’m a very good mediator and arbitrator,” he said at the start of a meeting in Hanoi with Vietnam’s president, Tran Dai Quang.
Last year, Mr. Duterte called for a “separation” from the United States, threatened to expel American troops and accused the Central Intelligence Agency of plotting to kill him. When asked how he would respond if the American president were to criticize his antidrug campaign, Mr. Duterte replied with a vulgar epithet to describe Mr. Obama, who was president at the time.
Mr. Roque, the spokesman, said that Mr. Duterte changed his tune after seeing the value of United States help in Marawi.
“He hasn’t been criticizing the United States lately,” Mr. Roque said in an interview. “He looks forward to closer ties with the United States.”
Mr. Trump, in fact, has been tied to the Philippines for years through his business dealings.
The president’s brand arrived in the Philippines well ahead of him: Trump Tower at Century City, a $150 million, 57-story residential building has been under construction since 2012 in metropolitan Manila. It is one of several international business deals that pose potential conflicts of interest for Mr. Trump.
The tower is being built by Jose E.B. Antonio, a Manila developer. Days before Mr. Trump was elected, Mr. Duterte named Mr. Antonio an envoy to the United States for trade, investment and economic affairs.
“I’ve always loved the Philippines. I think it’s just a special place, and Manila is one of Asia’s most spectacular cities,” Mr. Trump was quoted as saying on the Trump Tower website last year. The comment has since been removed.
But no words could please Mr. Duterte more than Mr. Trump’s support of the Philippines’ antidrug campaign.
Mr. Duterte won election on a promise to kill drug users and said that the fish in Manila Bay would grow fat feeding on their corpses. In the early months of the antidrug campaign, the police said that thousands of drug users had been killed. But as the extrajudicial killing has continued, they have refused to release the death toll.
Mr. Duterte won election last year with 39 percent of the vote, but his popularity soared after the killings began. While his support rating has declined in recent months, it still stood at 67 percent in September, according to a survey by the nonprofit Social Weather Stations.
While past American presidents have used meetings with foreign leaders to promote human rights, activists have little expectation that Mr. Trump will raise the extrajudicial killings with Mr. Duterte.
“I strongly suspect we will see an alpha-male bromance between the two,” said Phelim Kine, the Human Rights Watch deputy director for Asia. “A lot of the issues that underpin the U.S.-Philippine relations will go unaddressed, and one of those will be rule of law.”
Mr. Duterte has bristled at any criticism of his drug war. Speaking to Filipino workers in Danang, Vietnam, on Thursday, he lashed out at Agnes Callamard, the United Nations special rapporteur on extrajudicial, summary or arbitrary executions.
“This rapporteur, I will slap her in front of you. Why? Because you are insulting me,” he said in a speech sprinkled with expletives.
He also boasted of killing a man, as he often has in the past. Typically, there is little evidence to support his claims.
“At the age of 16, I have already killed,” he said. “A human. I stabbed him because he stared at me.”
Mr. Duterte also offered to host an international summit on human rights and compared himself to Satan. “I am the new toughie here in hell,” he said.
But in the coming days, for a more international audience, Mr. Duterte is likely to talk about what he can do to take a bigger role in the region’s most important issues. As chairman of Asean, Mr. Duterte wants to be a regional power broker who can help negotiate with North Korea, said Mr. Heydarian, the political scientist.
Within days of his April phone call with Mr. Trump, Mr. Duterte revealed that he had phoned President Xi Jinping of China at Mr. Trump’s request to discuss how to contain the North Korean nuclear threat.
“He is trying to punch above his weight, but everyone should welcome that,” Mr. Heydarian said. “Asean is one of the last bridges North Korea has to the international community.”
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