Mr Trump made the comments as they walked together to a larger meeting along with officials from their delegations.
"Past practices and prejudices were obstacles on our way forward, but we overcame all of them and are here today", Kim said. Seoul lives under constant threat of an attack by North Korea, and the country's leadership has been adamantly promoting diplomatic talks in order to avoid a full-blown conflict, especially as Pyongyang appeared closer to developing a nuclear weapon that could fit on an intercontinental ballistic missile.
Pompeo, who led the outreach as Central Intelligence Agency director, traveled twice to North Korea for preliminary talks. It's aimed at settling a standoff over Pyongyang's nuclear arsenal.
He has said he would size up Kim "within the first minute" of their meeting. He bounced to the Singapore summit after a tempestuous G-7 summit where the U.S. was isolated from its key European partners as never before and Trump even derided his Canadian host, a paragon of liberal democracy, as "dishonest" and "weak".
Several hours later, camera crews captured Kim and his entourage entering another luxury hotel on the island: the Marina Bay Sands - a 55-floor hotel and entertainment mecca with an infinity pool, lookout point, and the Ce La Vi bar and restaurant on the rooftop.
Trump planned to speak to reporters after concluding the summit, the White House said.
Officials of the two sides held last-minute talks to lay the groundwork for the summit of the old foes, an event nearly unthinkable just months ago, when they were exchanging insults and threats that raised fears of war.
One US official said the two sides were working to craft a joint US-North Korea "statement of understanding" that could be released after the talks. Trump traveled to Singapore from Canada, where he a meeting with other world leaders. This contrasted with Kim, who had comparatively less to lose, having already scored a major win through Trump's agreement to meet him.
In a video footage, Trump was seen leaving the Paya Lebar Air Base tarmac in the Presidential Beast, a vehicle that is flown around the globe for a US President's visits. They only ever met with former United States presidents, a symptom of six decades of hostility between the U.S. and North Korea, which remains a pariah in the eyes of the West not just for its nuclear and missile threats but for flouting worldwide norms of diplomatic behaviour. Past nuclear deals have crumbled over North Korea's reluctance to open its doors to outsiders.
"Bad idea", tweeted Paul Haenle, a former China director at the White House National Security Council in the Obama and George W. Bush administrations.
"Trump is a gambler and he's gambling on being able to rein in North Korea like a parent does to naughty child", Leong said.