"In Davao, I used to do it personally. Just to show the guys that, if I can do it, why can't you?" Duterte said.
"And (I'd) go around Davao with a motorcycle, with a big bike around and I would just patrol the streets and looking for trouble also. I was really looking for an encounter so I could kill."
He made the remarks at the Wallace Business Forum in Manila on Monday.
Since taking power in June, Duterte has waged a brutal "war on drugs." The crackdown has been linked to more than 5,900 deaths in less than six months.
The President's office has been contacted for comment.
'I have this migraine every day'
Speaking at the same forum, Duterte told business leaders he had been using the painkiller fentanyl to relieve severe pain after a "bad slip."
"I have this migraine every day. I had a bad slip ... I hit my head on the cement. I have a lot of issues with my spine," he said on Monday.
Duterte said he had been using more than the recommended dose of fentanyl until his doctor stopped him.
"I was only given a fourth of (the whole patch), but no more, because of course my doctor learned that I was using the whole patch because I felt better," he said.
"When he knew it, he made me stop and he said, 'The first thing you would lose is your cognitive ability.'"
In addition to the ongoing pain, Duterte said he suffered from Buerger's disease, due to his history of smoking. According to the Mayo Clinic's website, Buerger's disease, thromboangiitis obliterans, is a "rare disease of the arteries and veins in the arms and legs" that can lead to clots in blood vessels.
Duterte accused in senate hearing
Allegations that Duterte had been personally involved in killings in Davao were previously made at a senate inquiry set up to look into extrajudicial killings during the President's drug crackdown
Self-professed hitman Edgar Matobato told the committee he saw Duterte unload two magazines of an Uzi submachine gun into a National Bureau of Investigation official
"He must have finished 200 bullets," Matobato said in September.
The hitman claimed more than 1,000 people had been killed by death squads during Duterte's time as mayor.
The senate inquiry was scrapped and investigations stopped in October
, after the committee's head and Duterte critic, Sen. Leila De Lima, was replaced.
Philippines leader 'deliberately' avoided Obama
Duterte is no stranger to controversy -- he's frequently made headlines in the past year for his public statements.
Before an international summit in September, he called US President Barack Obama a "son of a bitch," while denouncing US condemnation of his war on drugs.
During the same speech this week in which he admitted to killing people, Duterte said he had deliberately avoided Obama at the Laos summit
to dodge an "awkward situation."
"I would not know if he would accept my gesture of a handshake," said Duterte.