"Together we have in our power to finally liberate this region and the world from this very serious nuclear menace, but it will require collective action, collective strength and collective devotion to winning the peace", Trump said.
Later, after a bilateral meeting with Vietnamese President Tran Dai Quang, Trump was asked at a joint news conference whether he thought it really was possible to be friends with Kim.
The comments are likely to go down extremely badly in Pyongyang, with North Korea extremely sensitive to any remarks - even if not meant to be taken seriously - that it sees as disrespectful to its rulers.
It comes on the same day Rodong Sinmun, the regime-run newspaper, warned the North would "surely win in the showdown" with the USA and South Korea.
"Unusual things happen in life", Trump said. The statement was issued in response to a speech delivered by Trump in South Korea's National Assembly on Tuesday, where he stressed that the U.S. should not be underestimated, and that North Korea's new weapons might be putting the regime in more, rather than less danger.
The post came in response to the country's foreign ministry calling Trump "an old lunatic" over his speech in South Korea.
North Korean officials described Trump's trip as "nothing but a business trip by a warmonger to enrich the monopolies of the United States defense industry". Trump said he also spoke while in Vietnam earlier this weekend with Russian President Vladimir Putin about the North Korea issue.
Town told ABC News that if Pyongyang conducted a test during or following Trump's trip, it would likely be with a Hwasong-14, what the USA refers to as the KN-20 - a two-stage intercontinental ballistic missile (ICBM).
Trump's visit to Beijing last week Xi reiterated that China would strive for the denuclearization of the Korean peninsula but offered no hint it would change tack on North Korea, with which it fought side by side in the 1950-53 Korean war against USA -led forces.
In the White House briefing room last week, Trump's national security adviser H.R. McMaster told reporters the administration would wait "a few months" before reassessing their strategy.
"And this artificial Democratic hit job gets in the way", Mr Trump said.