The two world leaders started the new round of negotiations by having dinner at the five-star the Sofitel Legend Metropole hotel on Wednesday.
“I think we’ll be very successful,” Trump said, adding that he and Kim have a “great relationship.”
The US president asserted that he “thought the first summit was a great success,” although his opponents believe it has not born any tangible results on the path to demilitarization on the Korean Peninsula, Presstv reported.
“Your country has tremendous economic potential, unbelievable, unlimited,” he said. “I look forward to watching it happen and to helping it to happen.”
US Secretary of State Mike Pompeo and acting chief of staff Mick Mulvaney as well as North Korean Foreign Minister Ri Yong Ho and nuclear negotiator Kim Yong Chol also attended the dinner.
Trump refused to answer a question about his former personal attorney Michael Cohen was about to deliver testimony accusing Trump of being a "conman," a "racist" and a "cheat."
However, ahead of the summit, Trump took to Twitter to slam his testimony before the US House of Representatives.
"Michael Cohen was one of many lawyers who represented me (unfortunately). He had other clients also," Trump tweeted from Vietnam. “He was just disbarred by the State Supreme Court for lying & fraud. He did bad things unrelated to Trump. He is lying in order to reduce his prison time. Using Crooked’s lawyer!” Trump said, referencing Cohen adviser Lanny Davis, who used to work for former US President Bill Clinton.
Cohen, Trump's longtime fixer, made payments during the 2016 campaign to two women – adult film actress Stormy Daniels and former Playboy model Karen McDougal – to silence them from speaking publicly about affairs they had with Trump.
His testimony comes at a time that Trump is trying to resolve conflict with Pyongyang.
The US has been engaged in diplomacy with Pyongyang after a summit between Trump and Kim in Singapore last June, but with little progress.
According to the White House, the second day of the summit would begin by a 45-minute one-on-one meeting with the North Korean leader.