DAVAO CITY, Philippines — President Rodrigo Duterte relishes the image of killer-savior. He boasts of killing criminals with his own hand. On occasion, he calls for mass murder.

Speaking of the drug addicts he says are destroying the Philippines, he said, “I would be happy to slaughter them.”

Mr. Duterte and his friends have long cultivated legends of his sadistic exploits, like throwing a drug lord from a helicopter and forcing a tourist who violated a smoking ban to eat his cigarette butt at gunpoint.

It is a thuggish image that Mr. Duterte embraces.

Whether Mr. Duterte has done what he says — the killings he claims to have carried out are impossible to verify — he has realized his gory vision in national policy. First as a mayor, now as president of the Philippines, he has encouraged the police and vigilantes to kill thousands of people with impunity.