In a separate bilateral meeting with Duterte, Trump said he and other leaders had a "tremendous time" during the gala dinner.
"President Trump has arrived in the Philippines to attend the 31st ASEAN Summit and Related Summits".
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.
A Philippines government spokesman later said human rights were not raised but White House spokeswoman Sarah Sanders said the topic was mentioned briefly.
"After the November 8 National Assembly speech, South Koreans are shedding their image of Donald Trump who haphazardly sees South Korea just another faraway country he does not want to understand", he said.
North Korean officials described Mr. Trump's visit as "nothing but a business trip by a warmonger to enrich the monopolies of the US defense industry".
Trump, for his part, claimed that he "had a great relationship" with the Philippine president, who stands accused of having ordered hundreds of extra-judicial killings in the name of fighting a war on drugs.
"I just wanted to congratulate you because I am hearing of the unbelievable job on the drug problem", Trump said in the April 29 phone call. He said there had been a "rather lengthy discussion of the Philippine war on drugs".
He tried to have it both ways Sunday on the issue of Russian interference in last year's presidential race, saying he believes both the USA intelligence agencies when they say Russia meddled and Russian President Vladimir Putin's sincerity in claiming that his country did not. Modi says relations between the US and India are "growing very rapidly" and "getting deeper and more comprehensive".
Handshakes must be awkward, full stop, if you have tiny baby hands - but even so, Donald Trump looks in agony in this group handshake shot.
Trump was meeting Monday with Indian Prime Minister Narendra Modi and dining with Australian Prime Minister Malcolm Turnbull ahead of the East Asia summit in Manila. But Trump's rapport with Duterte comes during a time when Duterte is being criticized around the world for approving extrajudicial killings in his war on drugs. "What the president is trying to do right now is recognize that the gravest threat that America faces is North Korea developing nuclear weapons".
Mr. Duterte's actions have alarmed human rights advocates, who say as many as 9,000 people have been killed in the crackdown on drug trafficking.