The international criminal court’s chief prosecutor has said she is “deeply concerned” about reports of extrajudicial killings of suspected drug dealers and users in the Philippines.

Fatou Bensouda also said that statements by “high officials” in the Asian nation “seem to condone such killings”.

Bensouda’s written statement appeared to be aimed as a blunt warning to the Philippine president, Rodrigo Duterte, whose anti-drug crackdown has left an estimated 3,000 people allegedly involved in the drug trade dead.

The Philippines is a member state of the international criminal court, the world’s first global court prosecuting war crimes and crimes against humanity, so crimes committed there could be prosecuted at the institution, which is based in The Hague.

“Any person in the Philippines who incites or engages in acts of mass violence including by ordering, requesting, encouraging or contributing, in any other manner, to the commission of crimes within the jurisdiction of the ICC is potentially liable to prosecution before the court,” Bensouda said.

In the Philippine capital, Manila, Duterte exuded confidence in a speech late on Thursday, saying he could easily parry any criminal investigation into the killings. He said he had written letters to invite the US president, Barack Obama, and secretary of state, John Kerry, and UN and EU officials to the Philippines to investigate him, but warned that he would publicly humiliate them by disproving their allegations.

As he had been a trial lawyer for eight years, “they cannot be brighter than me, believe me”, he said, adding that after he had been investigated, he should be allowed to grill his inquisitors.

“I will play with you in public. I will ask five questions that will humiliate you. And I will ask 10 questions for you to agree with me,” Duterte said in a speech at a business conference. “It would be a spectacle. You better watch it all … It will give you an entertainment.”

EU lawyers alleging he may be criminally liable for threatening criminals with death are “idiots”, Duterte said. He has said there is no Philippine law barring presidents from doing that.

Human rights advocates, however, say Duterte swore during his inauguration in June to ensure the execution of Philippine laws, some of which prohibit serious threats, especially death, towards people. The constitution also prohibits any cruel and inhumane punishments, including the death penalty.

Bensouda said her office would closely monitor developments in the Philippines in coming weeks with a view to establishing whether she should open a preliminary investigation.

Since becoming president in June, Duterte has drawn widespread criticism for his country’s deadly war on drugs.

Last week, the White House spokesman Josh Earnest said the US remained “deeply concerned by reports of widespread extrajudicial killings by or at the behest of government authorities in the Philippines. The use of that kind of tactic is entirely inconsistent with universal human rights and the shared values of our two countries.”