Duterte let loose with the crude insult two days after the major US newspaper wrote an editorial headlined: "Let the World Condemn Duterte", and which slammed the killings of thousands of Filipino drug suspects.
"New York Times, asshole," Duterte told reporters at Malacanang presidential palace minutes after receiving Brunei's Sultan Hassanal Bolkiah, the first of nine Southeast Asian leaders to arrive for the two-day summit starting Friday.
Duterte, responding to a query about the editorial, also accused the newspaper of ignoring US military abuses around the world and said the paper should stop publishing.
The New York Times called for the court to launch a preliminary investigation.
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"(This) would send an unmistakable signal to Mr. Duterte that he may eventually have to answer for his crimes, and would encourage governments to take measures against him, such as imposing tariffs on Philippine goods," it said.
Duterte, 72, easily won elections last year after vowing to kill tens of thousands of criminals and stop what he said was the Philippines' descent into a narco-state.
Duterte, who denies the allegations of summary killings and insists police only kill in self defence, on Thursday dared the International Criminal Court to pursue the case.
"Go ahead with the trial and let us see," he said, as he repeated his disdain for human rights.
"You know human rights (campaigners), I am not a worker for human rights," said Duterte, who frequently uses foul language against his critics.
Duterte also renewed his verbal assault on two major Filipino media outlets that have been critical of his drug war.
He also accused the owners of the Philippine Daily Inquirer of corruption, alleging they had illegally acquired government property in Manila's financial district too cheaply.