The Filipino president made the claims at a meeting with business leaders at the presidential palace on Monday.
Duterte said: "In Davao I used to do it personally. Just to show to the [police] that if I can do it, why can't you."
"And I'd go around in Davao with a motorcycle, with a big bike around, and I would just patrol the streets, looking for trouble also. I was really looking for a confrontation so I could kill."
Duterte's comments echo a statement he made in 2015 where he claimed he'd killed three men suspected of rape.
Senators Leila de Lima and Richard Gordon have condemned the president's remarks.
De Lima told CNN: "That is betrayal of public trust and that constitutes high crimes because mass murders certainly fall into the category of high crimes. And high crimes is a ground for impeachment under the constitution."
Gordon added: "When he says that, he's opening himself up, so what's the legal way, then go ahead and impeach him."
But Duterte ally Justice Minister Vitaliano Aguirre called Duterte's comments "hyperbole".
"He always exaggerates just to put his message across," Aguirre said.
Since Duterte's election in May, Amnesty International estimated that more than 3,000 people have been killed by police and vigilantes in the president's crackdown on drug dealers and addicts.
He has previously defended his hardline stance on drugs, once saying: "Hitler massacred three million Jews... There's three million drug addicts. I'd be happy to slaughter them."