One of the new challenges for Mr. Obama, and one for his successor, will be how to deal with Mr. Duterte. The police in the Philippines say they have killed about 1,000 suspects in the antidrug campaign, and about 300 people have been killed by vigilantes. Rights groups have urged the United States to do something about the situation.

“It’d be difficult for us to overstate how grave the situation has become in the Philippines,” said John Sifton, the deputy Washington director of Human Rights Watch. “At this rate, we’re talking about over 6,000 people dead by the end of the year.”

But the Philippines is an American ally and a bulwark against Chinese military gains in the South China Sea. By that calculus, the United States cannot afford to alienate Mr. Duterte. Philippine analysts say that Mr. Duterte is on good terms with Chinese business executives who invested in Davao, the city where he served as mayor, and that he may be open to negotiating with Beijing over the South China Sea.

Under American legislation known as the Leahy Amendment, Washington is obliged to cut off assistance to Philippines law enforcement units that are suspected of human rights abuses. But Antonio La Viña, a professor of government at Ateneo de Manila University, said the threat of such a sanction was unlikely to be effective.

“The truth is that the Philippines has the money to modernize our military,” he said.

Mr. Obama is the first sitting American president to visit Laos, and he has sought to promote reconciliation with the nation, on which the United States dropped more than two million tons of bombs at the height of the Vietnam War.

But he is also being called on to press Laos’s repressive government — a traditional ally of China — on the case of Sombath Somphone, a civil rights campaigner and American-trained agriculture specialist who disappeared at a police checkpoint in the capital, Vientiane, four years ago. Mr. Obama will also have to decide how hard to push concerns about human rights with other leaders at the meeting, several of whom are being wooed by China.