United States President Donald Trump praised Philippine President Rodrigo Duterte for doing an "unbelievable job on the drug problem" during a phone conversation last month, the New York Times reported, quoting a transcript of the call.

The two leaders also talked about North Korea and China's potential influence, the New York Times said, quoting parts of a Philippine transcript of the April 29 call that was circulated on Tuesday, under a "confidential" cover sheet, by the Americas division of the Philippine Department of Foreign Affairs.

According to the Times, a senior Trump administration official in Washington, who was not authorised to publicly discuss the call and insisted on anonymity, confirmed the transcript was an accurate representation of the call between the two leaders.

Almost 9,000 people, many small-time users and dealers, have been killed in the Philippines since Duterte took office on June 30. Police say about one-third of the victims were shot by officers in self-defence during legitimate operations.

"I just wanted to congratulate you because I am hearing of the unbelievable job on the drug problem," the New York Times quoted Trump as saying, based on the transcript of the April 29 call. “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 won a May 2016 election by a huge margin and is often compared with Trump, having himself been the alternative candidate from outside of national politics.

Reuters could not immediately verify the Times' account. But on May 2, after the phone call, Duterte's spokesman, Ernesto Abella, said Trump was very much aware of the criticism of Duterte, but had praised him for "doing a great job considering the weight and the enormity of the conditions in the Philippines".

The end of the phone conversation, according to the Times, centred on a first meeting between the two leaders.

Trump plans to attend an Association of Southeast Asian Nations (ASEAN) summit in Manila in November.

In the conversation, Trump twice invited Duterte to "come to the Oval Office," the Times reported.