More than 3,900 people have been killed in a war on drugs that Mr Duterte declared when he took office previous year.
Duterte's aggressive crackdown on drug traffickers and users in the Philippines has resulted in thousands of extrajudicial murders.
Police have killed nearly 4000 people in operations throughout the Philippines.
Trump and Duterte were joined by more than a dozen other leaders from Southeast Asia, Australia, Canada, Russia and India.
When White House reporters traveling with Trump asked whether the issue of human rights had come up at a meeting between the two presidents Monday, both Trump and Duterte declined to respond. While human rights groups were pressing the US President to take a tough stance on Duterte's bloody war on drugs, the issue reportedly did not see the prime light during their discussion.
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Mr Duterte, who once referred to Barack Obama as a "son of a b****" began the talks by telling Mr Trump: "We are your ally".
Mr Trump replied: "We've had a great relationship. And the ASEAN (Association of South East Asian Nations) conference has been handled beautifully by the president in the Philippines", according to Reuters reports.
But rather than rebuke Duterte's drug war killings, Trump praised him, according to a leaked transcript of a phone call between the two men earlier this year. "This is the bilateral meeting".
"The conversation focused on ISIS (Islamic State), illegal drugs, and trade".
However, the White House's version of events contradicts that of the Philippines' statement, which said that "there was no mention of human rights".