Speaking to reporters, Duterte said the Callamard has no right to tell him on how his administration should deal with the country's drug problem.
"She's son of a b****. Tell her, do not threaten me. She's son of a b****. She's a stupid. Where does she come from? What is [her] nationality?" Duterte said in an interview here in San Fernando, Pampanga.
"It will continue to emerge [drug-related deaths]. Even in your country, it happens. You are stupid. That's why your country is being bombed every day," he added.
Callamard, who hails from France, has repeatedly criticized the Duterte administration's drug war that resulted in the deaths of thousands of drug offenders since the firebrand President assumed office in June 2016.
In a series of tweets, Callamard called on Duterte to make sure that Kian Loyd Delos Santos, who was killed in an anti-drug operation in Caloocan City on August 16, is the "last" victim of "cruel" anti-narcotics war.
"My heartfelt condolences to Kian's family and to all families victimized by this cruel war. Make his death the last," she said on Twitter.
Furious by Callamard's remark, Duterte hit back at the UN envoy by citing the alleged "indefinite" detention of criminals in France.
"There, they can detain a person almost indefinitely under the French law. And the French law says if you are guilty, and you have to prove your innocence," he said.
The Chief Executive also challenged Callamard anew to visit the Philippines and investigate his administration drug war.
"Go here and see the situation. Do not ever give me that kind of s***. This is the Republic of the Philippines, not a French territory. She's stupid because she's not listening to what I'm saying," he said.
Duterte earlier invited Callamard to go to the Philippines to look into the drug-related deaths that have been recorded under his watch.
The invitation to Callamard, however, is still pending after several conditions set by the Duterte administration were not met.
Meanwhile, Duterte met the family of Delos Santos at Malacañang Palace after his public engagement in the City of San Fernando.
As of press time, Duterte's meeting with Delos Santos' parents is ongoing. Malacañang is yet to provide details regarding the meeting.
The President earlier vowed to punish Caloocan policemen who shot and killed Delos Santos, if results of the investigation show that his killing is a "rubout."
On August 25, the victim's parents filed murder complaints against Caloocan City Station 7 Police Chief Inspector Amor Cerillo, Police Officer (PO) 3 Arnel Oares, POs 1 Jeremiah Pereda and Jerwin Cruz, and several John Does.
The four police officers were relieved from their respective posts and placed under restrictive custody.