The UN human rights chief has asked Philippine authorities to launch a murder investigation after the president, Rodrigo Duterte, claimed to have killed people in the past, and to examine the “appalling epidemic of extrajudicial killings” committed during his anti-drug crackdown.

Zeid Ra’ad al-Hussein said the country’s judicial authorities “must demonstrate their commitment to upholding the rule of law and their independence from the executive” by investigating the president. He said it was “unthinkable for any functioning judicial system not to launch investigative and judicial proceedings when someone has openly admitted being a killer”.

Since taking office in June, Duterte has overseen a crackdown on the illegal drug trade that has left more than 6,000 people dead. Government officials have defended police actions during the crackdown.

Philippines president Rodrigo Duterte says he personally killed criminals Read more

Duterte has claimed in recent speeches that as a mayor in southern Davao city in 1988, he killed three suspected kidnappers in a firefight where he was backed up by three police officers. He later said he was unsure whether it was the bullets from his M16 rifle that killed the suspects.

Duterte has also suggested that he used to roam around Davao on a motorcycle looking for criminals to kill so that police would emulate him. “In Davao I used to do it personally. Just to show to the guys that if I can do it, why can’t you?” Duterte said last week. “I go around in Davao with a motorcycle, with a big bike, and I would just patrol the streets and looking for trouble also. I was really looking for an encounter to be able to kill.”

Hussein, the UN high commissioner for human rights, said Duterte’s acts “directly contravene the rights” enshrined in the Philippine constitution and “also violate international law”. He said Duterte’s encouragement of others to kill may constitute incitement to violence, and expressed concern about Duterte’s assurances that police officers who committed human rights violations would be immune to prosecution.

“The perpetrators must be brought to justice, sending a strong message that violence, killings and human rights violations will not be tolerated by the state and that no one is above the law,” he said.

The Philippine justice secretary, Vitaliano Aguirre II, has defended Duterte, saying the president often exaggerates tales of killing criminals to send a warning to lawbreakers. Aguirre said Duterte may have been resorting to hyperbole in his description of his motorcycle tours of Davao.

Duterte has previously threatened to withdraw the Philippines from the UN for its criticism of his drug crackdown, describing the world body as powerless in the face of genocidal killings in other places.