Duterte continued, according to the Associated Press, saying that members of the public can kill drug dealers who resist arrest or threaten citizens with weapons.
"Shoot him and I'll give you a medal," Duterte said, according to the wire service.
The former mayor won last month's presidential election in a landslide, campaigning on an anti-crime and anti-corruption platform. But the brash politician, dubbed the "Death Squad Mayor" by Human Rights Watch, has been the subject of international scorn, particularly for incendiary comments about journalists and about the 1989 rape and killing of an Australian missionary during a prison riot.
He will be sworn into office June 30.
Duterte has previously offered bounties to military and police officials for every drug lord they turn in or capture. "I'm not saying that you kill them, but the order is dead or alive," Duterte said in a May televised news conference.
On Saturday, he said that his anti-crime campaign would be a "bloody war," according to AFP.
It's unclear what his pledges will mean in practice. He reportedly said Saturday that he would offer $107,000 for dead drug lords, and there have been reports of local elected leaders paying police officers for killing drug traffickers.
The Philippines has become both a destination and a transit point in the methamphetamine drug trade. Large shipments of the drug, known locally as "shabu," go through the country.
According to official Philippine government data, most people in residential and nonresidential drug treatment and rehabilitation facilities are there for methamphetamine hydrochloride.
Corruption has made it difficult to battle the nation's drug problem; law enforcement officials and members of the media have accused politicians and government officials of receiving kickbacks from drug traffickers, according to a U.S. State Department report.
On Saturday, Duterte spoke about corrupt police officers and demanded that three police generals, whom he did not identify, resign.
"[To] all police who have cases and are wanted now, if you are still involved in drugs, I will kill you," he said, according to a CNN Philippines translation. "Don't take this as a joke. I'm not making you laugh."
Human rights groups have expressed alarm over Duterte's rhetoric and positions. He has publicly backed death squads and has previously threatened to kill suspected criminals.
After his comments last month that most assassinated journalists deserved to be killed, the National Union of Journalists of the Philippines declared the incoming president had essentially "declared open season to silence the media, both individual journalists and the institution, on the mere perception of corruption."