"The future of this region and its attractive people must not be held hostage to a dictator's twisted fantasies of violent conquest and nuclear blackmail", he said during a speech in Vietnam to the annual Asia Pacific Economic Cooperation (APEC) forum.
Tensions over North Korea's weapons programme have surged in recent months, as Pyongyang carried out a sixth nuclear test - by far its largest to date - and test fired dozens of missiles, some capable of reaching the U.S. mainland.
Mr Trump offered North Koreans a "path towards a much better future", having urged the regime to "come to the table" and "make a deal" over its nuclear programme.
North Korea has dominated Trump's trip, which has so far swept in Japan, South Korea, China and Vietnam.
In that sense, the 60-day freeze is a low bar for Kim Jong Un, who prefers to launch during the spring when the US and South Korea engage in their annual military drills.
In this image released by the U.S. Navy, the aircraft carrier USS Carl Vinson, flanked by South Korean destroyers, from left, Yang Manchun and Sejong the Great, and the U.S. Navy's Wayne E. Meyer and USS Michael Murphy, transit the western Pacific Ocean Wednesday, May 3, 2017.
Family of 4 found dead in Mapleton home
They were found after one family member failed to show up for work and neighbors noticed the family cars hadn't moved. "Once inside officers found four individuals that were deceased from what appears to [have been] gunshot wounds".
North Korea fears the USA wants it to be merged with South Korea.
He also referenced the visit came a year on from his victory in the USA election, adding he would be "celebrating" the achievement with the South Korean people.
They will aim to enhance combined operation and aerial strike capabilities and also display "strong will and firm military readiness to defeat any provocation by North Korea with dominant force in the event of crisis", Seoul's military said in a statement.
It is the first such United States triple-carrier drill in the region for a decade.
The US has been sending its strategic assets, also including long-range bombers, to the region more frequently for patrols or drills amid accelerating North Korean efforts to expand its nuclear weapons program.
In a statement, the Chinese foreign ministry said China and the USA had a "common goal" for the Korean peninsula, and the two nations would step up communication about it.
Joseph Yun, the State Department's top North Korea official, told the Council on Foreign Relations on October 30 that the U.S. would resume direct dialogue with Pyongyang if it ceased missile tests for 60 days, sources told The Washington Post.