Trump and President Duterte are set to hold a bilateral meeting on the sidelines of the summits.
Claiming he was being serious, Duterte said: "Really, it's true".
Speaking to the local Filipino community in the Vietnamese city of Danang on Thursday, Duterte also threatened to slap a United Nations rights rapporteur if he met her, and used obscene language to hit back at critics of his deadly drugs crackdown.
Mr Duterte made the assertion on Thursday in a meeting with the Filipino community in Da Nang, Vietnam, where he and leaders from other Pacific Rim countries were gathered for a meeting of the Asia-Pacific Economic Cooperation forum.
"At the age of 16, I had already killed someone. The US President's willingness to challenge the appalling record of President Duterte's "war on drugs" is a crucial test of his administration's commitment to upholding and defending human rights". "I think it was in jest". "The president uses colorful language when with Pinoys overseas", he added, referring to Filipinos.
"We want [Trump] to know that the students and the youth here shall not allow imperialist power to plunder and continually kill our people", the group's chairperson Kristine Cabardo told Philippines newspaper SunStar.
"Duterte will enjoy the gift of tacit silence from East Asian leaders on his murderous drug war during the upcoming summit", Human Rights Watch deputy Asia director Phelim Kine told AFP.
The Philippines National Police (PNP) has killed more than 3,800 alleged drug offenders and has paid others to kill thousands more in what may amount to crimes against humanity.
With both President Trump and Russian President Vladimir Putin scheduled to be in Vietnam for the APEC summit, the expectation has been that a meeting would take place, with Russia confirming one would happen, and weeks of preparation on both sides.
But critics warn the gesture has come to represent the brutalities of Duterte's drug war, which has claimed thousands of lives. "He is not the [head of the] Human Rights Commission", he said.
The 71-year-old has rarely taken kindly to criticism of his drug war.
"Like I said before, you will have to find a soldier or a policeman anywhere in the country where I ordered the killing of a man on bended knees, in surrender, or lying down", Duterte added.
Karapatan secretary-general Cristina Palabay said it was hypocritical for the two to even discuss the topic given their tracklist of human rights violations.