During a gala for the 20 world leaders in Manila to attend the annual Association of Southeast Asian Nations summit, Duterte took the microphone and sang the love song Ikaw, or You, in a duet with local pop star Pilita Corrales.
Trump's stop in the Philippines will be his last on his 12-day tour of Asia.
"We've explained that the United States is open for trade but we want reciprocal, we want fair trade for the United States", he said. The two men also shared a laugh in the meeting when Duterte called reporters "spies", the Associated Press reports.
Trump was standing on stage at the Manila summit alongside leaders including Philippine President Rodrigo Duterte, Russian Prime Minister Dmitry Medvedev and Vietnamese Prime Minister Nguyen Xuan Phuc when they crossed their arms for a traditional group handshake.
PM Modi is the second Indian Prime Minister to visit Manila since Indira Gandhi.
The two sides sealed four agreements and agreed to cooperate on counter-terror. Activists later held their protests about a kilometre away from the venue and burned a 13-foot (4-metre) effigy of U.S. President Donald Trump. His government says the police act in self-defense, but critics say executions are taking place with no accountability. Trump, by contrast, said on Monday he had a "great relationship" with Duterte.
On the ground, military operations continue to clear buildings for stragglers.