Asked if De Lima's arrest serves as a warning to administration critics, the President said unless they were involved in drugs they should not be afraid.
Human rights groups believe numerous others were extra-judicial executions committed in cooperation with the police - a claim the Duterte administration has vehemently denied.
"With this agreement, we can now push through with our new and bigger role in ending the illegal drugs scourge", Arevalo said.
"We are ready to go back to war if given orders by the President", he said.
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Presently, the lead agency handling anti-drug operations is the Philippine Drug Enforcement Agency (PDEA) with support from elements of the Armed Forces of the Philippines (AFP).
More than 8,000 people have been killed in the war on drugs since Duterte was sworn in nearly eight months ago, about 2,500 of whom were killed in official police anti-narcotics operations.
The national police chief, Ronald Dela Rosa, said on Monday that gains in the drug war had been lost because his force had been withdrawn.
The Philippine Drug Enforcement Agency, which took over the campaign when the police's war on drugs was suspended, will continue to supervise anti-illegal drug operations, Duterte said.
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At least 13 "high-value" detainees facing drug charges have escaped from a jail in northern Philippines, the latest in a series of prison breaks in the country, according to authorities. We will be informed in due time.
The military also plans to use its assets in assisting PDEA in counterintelligence build-up and investigation of government officials and groups linked to illegal drugs.
The PNP chief noted that since President Rodrigo Roa Duterte ordered a stop in the PNP's campaign against illegal drugs, the activities of drug syndicates seemed to have proliferated again. Duterte added he is leaving it up to the PNP to proceed with Oplan Tokhang and Project Double Barrel.
"And if you fight it out with me, I will kill you", Duterte said. However, it has emerged that since the halt of the police operations, there has been a near 20% rise in drug sales in the Philippines.
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"I would like to warn them, I will not spare you".