Mr Kim called the United States president "courageous" in return and said he was confident there would be an "excellent outcome that everyone welcomes".
The two leaders are due to hold a series of meetings at the Metropole which will begin with another one-on-one session lasting 45 minutes, according to the White House.
"The two men will sit down for about six hours today".
North Korean leader Kim Jong Un signaled during an unprecedented question-and-answer session with reporters that he is "ready to denuclearize", reaffirming a commitment long sought by the Trump administration and the worldwide community. Seoul a year ago walked back a proposal to lift some of its unilateral sanctions against North Korea after Trump's bluntly retorted Seoul could "do nothing" without Washington's approval.
Through his interpreter, Kim said, "It's too early to tell but I wouldn't say I'm pessimistic".
After last year's Singapore summit, and especially before this week's summit in Hanoi, North Korean internal propaganda has been busy promoting the idea that Kim deserves a prize, Radio Free Asia reported this week.
"North Korean welfare is a failure".
History appeared to have been made when Kim answered questions from a foreign journalist - nearly certainly for the first time ever.
Apart from the two state leaders, five people from each side are also taking part in the working dinner.
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Trump also plans to brief reporters in person on the outcome of this week's bargaining with Kim before heading back to Washington on Thursday evening.
One such site is the Yongbyon Nuclear Scientific Research Center, located a little more than 60 miles north of the North Korean capital of Pyongyang. But that would leave him with missiles, warheads and weapon systems, Pompeo said.
Now U.S. officials talk about simultaneous actions taken by both sides. Trump declined to restate that goal Thursday, insisting he wanted flexibility in talks with Kim. "I want my people to do the same".
There was disappointment and alarm in South Korea, whose liberal leader has been a leading orchestrator of the nuclear diplomacy and who needs a breakthrough to restart lucrative engagement projects with the impoverished North. Yonhap news agency said that the clock on the Korean Peninsula's security situation has "turned back to zero" and diplomacy is now "at a crossroads".
Soon after, as journalists were allowed to see the beginning of the final day of talks, Kim responded to several more questions from American reporters in the White House pool - including The Associated Press, Reuters and Bloomberg.
Possible outcomes could include a peace declaration for the Korean War that the North could use to eventually push for the reduction of US troops in South Korea, or sanctions relief that could allow Pyongyang to pursue lucrative economic projects with the South.
There was no indication of when Trump and Kim might meet again but the White House said the "respective teams look forward to meeting in the future".
Some experts on past U.S.
"We had a very successful first summit", Mr Trump said, standing alongside Mr Kim. They're no longer demanding an inventory of weapons up front.