"My orders are to kill you if you are caught and I will protect the police who kill you," Duterte said he told his 42-year-old son Paolo Duterte, vice mayor of the city of Davao, GMA News reported.
Paolo, who is known as Pulong, as well as the president's son-in-law, lawyer Manases Carpio, are accused of being involved in a Chinese transnational narcotics network that has been smuggling drugs through the Philippines Bureau of Customs.
Pulong and his brother-in-law have both denied the accusations against them, claiming that they are "baseless" and founded on "rumors."
During his Wednesday speech, Duterte reiterated warnings he had issued when he himself was still Davao City mayor and Paolo's alleged illegal activities were broached.
"I said before, if I have a child into drugs, you just kill them so no one can say anything," Duterte said.
Since Duterte won the 2016 presidential election, he has carried out a brutal "war on drugs" that has resulted in the death of more than 7,000 Filipinos and raised accusations of extrajudicial executions by police.
According to Human Rights Watch, almost 3,000 of the drug war killings have been committed by the Philippine National Police. The organization also says its research shows Philippines police are fabricating evidence to justify unlawful murders.