Trump also said he wanted to withdraw the United States troops stationed in the South, something he promised on the campaign trail, saying: "I'd like to be able to bring them back home".
The two leaders who will sit down for the world's most keenly watched political meeting this year have arrived in Singapore, setting in motion a series of events that could have lasting global ramifications.
"We had a really fantastic meeting", Trump said as he strolled out of the Capella Hotel side-by-side with the North Korean leader after their working lunch on Tuesday. Top of the line, very good.
Kim could be seen smiling as he looked inside the vehicle.
Kim was heard telling Trump through a translator: "I think the entire world is watching this moment".
"Rather than signing an unsubstantial agreement, Trump and Kim should be signing a real document based on worldwide law, the Treaty on the Prohibition of Nuclear Weapons". The two men were each accompanied only by an interpreter, raising concerns among experts.
While the Air Force One carrying Donald Trump landed in Singapore on Sunday evening, Kim Jong-un reportedly travelled by a Chinese plane, deployed for his personal use, and was received by Singaporean foreign minister.
North Korean leader Kim Jong-un has committed to "complete denuclearisation of the Korean Peninsula" in a joint text.
After briefly moving away from the media glare, Mr Kim and Mr Trump reappeared, walking together along a balcony and posing for pictures.
A woman walks past a cannon barrel stuffed with flowers in a symbolic gesture of peace at Fort Siloso in Singapore, as preparations continue for Tuesday's Trump-Kim summit.
The North Korean leader, however, provided Trump a chance for diplomatic redemption, no matter how fleeting. "Many people in the world will think of this as a scene from a fantasy.science fiction movie".
US President Donald Trump also "committed to provide security guarantees" to Pyongyang, apparently in return for Kim Jong Un's efforts towards denuclearization.
Trump's use of the term "provocative" marked a notable break with past US policy in itself.
According to Trump, it's a "very important" and "pretty comprehensive" document. We've overcome so many obstacles which blocked our eyes and ears, dragging our feet down due to the past history, prejudices.
Ahead of the meeting, Trump had said he would be able to work out within the first minute whether his North Korean counterpart was serious about making peace. We'll be doing something on it.More news: Andrew Garfield Dedicates His Tony Award to LGBTQ Community