In withdrawing from the court last year, Mr. Duterte said that the Philippine government had enough mechanisms in place to ensure that the justice system functioned properly. He also insulted the court and threatened to arrest Fatou Bensouda, a Gambian lawyer and the court’s chief prosecutor, if she entered the Philippines.

The court has been conducting a preliminary inquiry into accusations that Mr. Duterte and other Philippine officials committed mass murder and crimes against humanity in the course of the drug crackdown. That inquiry stemmed from a complaint filed by a Filipino lawyer representing two men who said they had been assassins for Mr. Duterte in Davao, the southern city where Mr. Duterte became mayor in the late 1980s.

A second complaint was filed in August by relatives of eight people killed by police officers in the drug war; they also accused Mr. Duterte of murder.

In their Supreme Court motion, the rights activists said that withdrawing from the court would deprive Filipinos of “effective remedies” against genocide and other crimes against humanity.

The petitioners argued that “those who kill with impunity will only be further emboldened.”

When Mr. Duterte took office in 2016, he vowed to end the scourge of drugs and dump the bodies of slain addicts and dealers in Manila Bay. Over 5,000 people have been killed by the police in what are often described as drug raids. Rights groups say many more have been killed by unofficial militias.