"I just wanted to congratulate you because I am hearing of the unbelievable job on the drug problem," Trump said, in a transcript of the call, according to the Times report. "Many countries have the problem, we have a problem, but what a great job you are doing and I just wanted to call and tell you that."
Duterte has waged a war the drug trade in his country, killing thousands, and alarming human rights groups around the world.
According to the Times, the released transcript came from the Philippines. The White House typically keeps such transcripts under wraps, although the Times says one senior administration official confirmed the general contents of the call.
The two leaders also reportedly discussed North Korea, before Trump invited Duterte to the White House.
"I will love to have you in the Oval Office, anytime you want to come," he said, according to the report.