MANILA—Departing Philippine leader Benigno Aquino III, who roundly criticized President-elect Rodrigo Duterte during the recent election campaign, said the reality of running the country should tame his successor’s violent instincts.

“We’re not a dictatorship; we’re bound by laws,” Mr. Aquino said in an interview Thursday, saying the hyperbole of the campaign trail would soon fade. Once he takes over on June 30, Mr. Duterte, who has promised to kill thousands of criminals to guarantee law and order, will “be fully grounded...