Duterte, who is waging an anti-drugs war that has left thousands dead, said last week that he helped police kill three suspected kidnappers early in the first of his several terms as mayor of the southern city of Davao.
UN rights chief Zeid Ra'ad Al Hussein said Tuesday that Duterte's killings, by his own admission, "clearly constitute murder" and Philippine judicial authorities must launch an investigation.
Duterte, known for his foul-mouthed outbursts, replied to Zeid's call in a speech Thursday with a stream of insults, describing the UN official as "either a joker or slightly unhinged" while stating that UN member-nations' contributions pay the UN officials' salaries.
"You, the officials sitting there. You assholes, we pay you your salary.
"You idiot, you do not tell me what to do. I am your employer and [you] do that, do it to a nation."
"You do not talk to me like that you son of a bitch. Only the Filipinos can call me a son of a bitch if I'm remiss in my job."
Philippine Commission on Human Rights chief Jose Gascon said earlier Thursday he had formed a team of investigators to look into alleged past killings by Duterte.
"Law enforcement agencies... must investigate as a matter of course any information that suggests that a crime may have been committed with the view to ensuring that perpetrators are ultimately held accountable should the evidence warrant it," Gascon said in a statement.
The commission is an independent government body that prosecutes law enforcers or other officials who commit torture, extrajudicial killings or violate Filipinos' constitutional rights.
New revelations
It had investigated then Davao mayor Duterte over allegations he ran death squads that killed more than a thousand petty criminals there.
Duterte has variously denied or confirmed the allegations. The commission did not file any criminal charges after completing its inquiry.
But Gascon said his agency had "reconstituted a team to further investigate [Davao death squads] to look into the new revelations and public admissions that may shed light on our previous findings."
"The team will look into any matter that may further shed light on the killings in Davao that was the subject matter of our previous investigation."
Duterte easily won presidential elections in May largely on a promise to eradicate illegal drugs in society by launching an unprecedented campaign in which tens of thousands of people would be killed.
More than 5300 people have died since he took office in late June, including 2124 at the hands of police. The commission has said it is investigating several cases where police were responsible.
Duterte insists police have not violated any law in killing drug suspects.
On Wednesday Duterte's spokesman said his admission about the killing of three people referred to "legitimate police action" but did not address the fact the then mayor was not a police officer.
