Still, he noted that decades of tension can not be resolved in one meeting, although, based on his interactions with their staff and meeting them personally, "both are supremely confident, both are hopeful".
The first handshakes and smiles set a tone for the rest of the day's meetings.
Trump's early exit will be his second from a summit in just a few days. Lighthearted comments from Trump.
Any downgrading of the U.S. military presence in South Korea would likely be resisted by the White House and unpopular in South Korea. That was to be followed by dark chocolate tarts, pastries and vanilla ice cream for dessert.
No word on denuclearization, though.
Rodman said he received a call from the White House saying that "Donald Trump is so proud of you". Critics have contrasted his rude treatment of close allies with his seemingly friendly encounter with a murderous dictator. Secretary of State Mike Pompeo, Chief of Staff John Kelly and National Security Adviser John Bolton will also be involved in bilateral meetings.
Trump will hold a press conference at 4 p.m. local time (6 p.m. AEST).
0159 Trump said at the group table that he and Kim "will solve a big problem, a big dilemma". "We can go fast, we can go slowly", Trump said.More news: Rafael Nadal vs Dominic Thiem, French Open 2018 men's final
More news: G7 row: Emmanuel Macron attacks Donald Trump's 'fits of anger'
More news: Origin Access Premier is EA’s New PC Games Subscription Service
At 9am Kim shook hands with Trump and greeted him in English: "Nice to meet you, Mr President".
For better part of an hour, Trump and Kim will square off one on one, alone but for a pair of translators. They are not responding to questions. The world saw it. Pyongyang has advocated for decades for a peace treaty to formally end the Korean War, rather than the armistice that has been in place for more than 60 years.
The media were then ushered out of the room.
On Monday night's The Ingraham Angle, Wallace said that it's "almost surreal" to see Trump and Kim, "who just months ago were launching verbal ICBMs at each other", standing together and shaking hands. "Old practices and prejudices worked against us but we overcame all of them and we are here today". "It's my honor, and we will have a terrific relationship".
0059 Trump is emerging from his vehicle and entering the hotel doors. He may be bringing his own armored limousine and bodyguards.
Yet the optimism about the summit - for which Trump seemed completely unprepared - is hardly warranted.
Restaurants and businesses in Singapore are cashing in on the summit, CBS News correspondent Ben Tracy reports.
0031 Kim's motorcade has arrived. His aides were on Twitter during the journey.
Kim Jong-un touring Singapore's Marina Bay Area, on a night-time stroll around some of Singapore's sights.
Dr Balakrishnan posted a photo on Facebook which showed the two parties celebrating Mr Trump's birthday early with a large cake.