Almost a year after the two leaders held a historic meet in Singapore, Trump and Kim met for the second summit in Vietnamese capital on Wednesday
The US president rejected any suggestion on if he was walking back on US demands for North Korea's denuclearisation.
Trump told reporters he thought the talks would be very successful, and asked if he was 'walking back' on denuclearisation, said 'no'.
At their historic first summit in Singapore last June, Trump and Kim had pledged to work toward denuclearisation and permanent peace on the Korean peninsula.
North and South Korea have been technically at war since their 1950-53 conflict, with the Americans backing the South, ended in a truce, not a treaty.
Asked if he would declare a formal end to the Korean War, which North Korea has long called for, Trump said, “We’ll see.”
In the run-up to this summit, Trump has indicated a more flexible stance, saying he was in no rush to secure North Korea's denuclearisation.
He repeated that on Wednesday, saying while some people believed the talks should be moving more quickly, he was satisfied.
Trump has held out the prospect of easing sanctions if North Korea does something "meaningful".
'Vietnam is thriving like few places on earth. North Korea would be the same, and very quickly, if it would denuclearise,' Trump said on Twitter ahead of the meeting. The potential is AWESOME, a great opportunity, like almost none other in history, for my friend Kim Jong Un. We will know fairly soon - Very Interesting!"
Trump and Kim are scheduled to hold a 20-minute, one-on-one chat followed by a dinner with aides.
Trump will be accompanied by Secretary of State Mike Pompeo and acting Chief of Staff Mick Mulvaney. Kim will be joined by his top envoy, Kim Yong Chol, and Foreign Minister Ri Yong Ho.