A spokesman for Duterte, however, said "there was no mention of human rights" and "no mention of extralegal killings".
He said what took place was a "rather lengthy discussion" of the Philippines' war on drugs "with President Duterte doing most of the explaining".
A joint statement says the two leaders "underscored that human rights and the dignity of human life are essential".
Duterte sang in a duet with a local diva Pilita Corrales, performing a popular song, "Ikaw" (You), which goes: "You are the love I have been waiting for".
Kine later said this photograph of Trump twisting his face as he held hands with Duterte over the weekend should "live in infamy". President Trump must also make clear that any future United States assistance to the country will be linked to clear progress in reforming the PNP and ending impunity in the police. Modi says relations between the USA and India are "growing very rapidly" and "getting deeper and more comprehensive".
President Donald Trump is wrapping up his extensive trip to Asia with an worldwide summit and one-on-one meetings with global partners, including his Philippine host who is overseeing a bloody drug war.
The handshake chain is a set piece of gatherings of the 10-member Association of Southeast Asian Nations (ASEAN), who are meeting with leaders from China, the US, Russia, New Zealand, Australia, India, Canada, Japan and South Korea. However, at some point into the banquet, Duterte, seated next to Trump in his formal Philippines long-sleeved white shirt, suddenly stood up and startled his guests with a vocal performance.
Philippine President Rodrigo Duterte will host world leaders in Manila from Sunday, hoping their presence will quieten worldwide criticism over his deadly drugs war, which rights groups say may be a crime against humanity.
Trump is teasing a "major statement" on trade and North Korea in Washington on Wednesday when he returns.