Political tensions deepened in the Philippines after the country’s justice secretary asked tens of thousands of President Rodrigo Duterte’s supporters who else they would like to see locked up, a day after police had arrested a prominent antigovernment senator.

“Who do you want next?” Vitaliano Aguirre II asked the huge crowd that gathered late Saturday in support of Mr. Duterte and his bloody war on illegal drugs.

“Trillanes,”...