The president's controversial war on drugs campaign has so far seen more than 9,000 civilians killed.
"My orders are to kill you if you are caught, and I will protect the police who kill you," Duterte said he told his son.
Paolo faced a senate hearing this month, accused of being involved with the triad gang. He faces allegations that he helped facilitate the shipment of ice into the country.
Paolo Duterte, the eldest son of President Rodrigo Duterte takes his oath in his continuing senate probe. Photo / AP
"Once and for all, I now have the time to deny any and all baseless allegations thrown against me," Paolo told the senators.
At the height of the Senate inquiry, Senator Antonio Trillanes accused Paolo of being a member of the Chinese triad, an organised crime group, citing intelligence information he said was provided by a foreign government. The young Duterte, Trillanes alleged, has a tattoo at the back that is the mark of a triad gang member.
Paolo acknowledged he has a tattoo during questionings but refused to show it, citing his right to privacy.