MANILA—The Philippine defense chief said Friday that he had suspended participation in any joint patrols with the U.S. of the disputed South China Sea, the first concrete sign of a crack in the military alliance following the election of President Rodrigo Duterte.

Defense Secretary Delfin Lorenzana also said he also would ask a small detachment of American troops providing counterterrorism assistance on the southern island of Mindanao to leave as the president requested. But he said that would happen only after the Philippine military can carry out such operations on its own, something that could take years.

Since taking office June 30, Mr. Duterte has caught U.S. officials and his own military off guard with seemingly off-the-cuff pronouncements with potentially far-reaching strategic implications. His aim, he said, is to loosen ties with the U.S. and give his Southeast Asian country a more “independent” foreign policy, with “new alliances” with China and Russia.

In the wake of several anti-American outbursts, defense officials had repeatedly said they were waiting to see whether the president’s words amounted to actual policy, while U.S. officials said they hadn’t been notified of any changes to the alliance.

The U.S. Embassy in Manila on Saturday confirmed the U.S. has not received any formal notification from Philippine officials regarding a halt to joint military patrols or exercises.