VIENTIANE, Laos—President Barack Obama canceled a planned meeting with Philippine President Rodrigo Duterte, in a rare diplomatic rupture that follows an outbreak of tensions between two close allies over the Philippines’ new drug war.

The White House said last week that Mr. Obama was planning to meet with Mr. Duterte during his trip to Laos for a summit of Asian leaders beginning Tuesday. The meeting would have been the first between the world leaders since Mr. Duterte took office in June.

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