Mr Duterte said last week he had helped police kill three suspected kidnappers while he was mayor of the southern city of Davao.
The United Nations Human Rights chief, Zeid Ra’ad Al Hussein, called for an investigation in the Philippines, saying the killings “clearly constitute murder”.
Now, the head of the country’s Commission on Human Rights, Jose Gascon, says he has formed a team of investigators to look into the matter.
“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,” Mr Gascon said in a statement.
Mr Duterte’s spokesman, Ernesto Abella, dismissed the UN call as “opinion”, and said the story about the killing of three people referred to “legitimate police action”.
But he did not address the fact that the then mayor was not a police officer.
Mr Duterte has been waging a tough campaign against drug dealers since winning the presidency.
More than 5,300 people have died since he took office in June, including 2,124 at the hands of the police.
Mr Duterte has insisted police have not violated any law by killing drug suspects.
The commission is an independent government body which can prosecute law enforcers or other officials who commit torture or extrajudicial killings, or violate constitutional rights.
It has already investigated Mr Duterte’s time as mayor of Davao after allegations he ran death squads that killed more than 1,000 petty criminals.
At various stages, Mr Duterte has denied and confirmed the allegations.
After completing its inquiry, the commission did not file any criminal charges.
:: The American singer-songwriter James Taylor has cancelled an upcoming concert in the Philippines in protest at the killings linked to the war on drugs.