"Why don't you give them a visit, pour gasoline on their homes and set these on fire to register your anger," Ronald dela Rosa said in a speech aired on television Friday.
"They're all enjoying your money, money that destroyed your brain. You know who the drug lords are. Would you like to kill them? Go ahead. Killing them is allowed because you are the victim."
Dela Rosa was speaking Thursday to several hundred drug users who had surrendered in the central Philippines.
Dela Rosa's comments followed Duterte's own controversial directives that have sparked criticism from the United Nations and human rights groups.
Duterte, 71, won May elections in a landslide on a vow to kill tens of thousands of suspected criminals in an unprecedented blitz that would eliminate illegal drugs in six months.
He promised on the campaign trial that 100,000 people would be killed and so many bodies would be dumped in Manila Bay that fish would grow fat from feeding on them.
Days after his election win, Duterte also offered security officials bounties for the bodies of drug dealers.
And when he took office on June 30, Duterte told a crowd in Manila: "If you know of any addicts, go ahead and kill them yourself as getting their parents to do it would be too painful."
The UN special rapporteur on summary executions, Agnes Callamard, said such directives "amount to incitement to violence and killing, a crime under international law".
However Dela Rosa and Duterte have insisted they are working within the law and their aides have dismissed some of their comments as merely "hyperbole" meant to scare drug traffickers.
- 'Sad, mad and sorry' -
After a barrage of bad headlines, Dela Rosa on Friday apologised for his remarks the previous day and described them as due to an "emotional outburst".
"Yesterday, I said that because I felt so bad. I was in front of those poor people, pushers and users, they looked like zombies. I was so mad, that's why I said that," he told reporters.
"I'm sorry if I said something unpleasant. Many people are reacting. I am very sorry. I am just a human being who gets mad."