Samsudin Dimaukom, the mayor of the southern town of Saudi Ampatuan, was one of more than 150 local government officials, judges and police identified by President Duterte earlier this year as being involved in the illegal drug trade.
The deadly crime war has claimed more than 3,800 lives and drawn criticism from the United States, the United Nations and international rights groups who have accused police of summarily executing suspects.
Police spokesman Superintendent Romeo Galgo said that Dimaukom and his security personnel opened fire after anti-narcotics police stopped their vehicles at a checkpoint on suspicion they were transporting illegal drugs.
Officers returned fire, killing the men in the town of Makilala, about 950 kilometres (600 miles) south of the capital Manila.
"Suspects (were) heavily armed and fired upon the law enforcers, which prompted them to fire back," Galgo said.
Dimaukom made a name for himself by funding the construction of a pink mosque in Saudi Ampatuan in a plea for peace in the town which has been wracked by violence.
Mr Duterte, who swept to power in May elections on a pledge to eradicate drugs, has described his critics as "fools" and said he is not breaking any domestic laws by threatening to kill criminals.
After returning from a trip to Japan late Thursday, he threatened to step up police killings of drug suspects.
"If my wish to get rid (of illegal drugs) in my country is not granted, you can expect about 20,000 or 30,000 more. There is a war going on," he said.
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