The US President is at Singapore's government house with the country's leader Lee Hsien Loong finalising preparations before the historic Trump-Kim summit.
Trump arrived in Singapore after another meeting with foreign leaders - a group of close American allies. Kim Yong Chol, the North Korean leader's right-hand man, and Vice Minister of Foreign Affairs Choe Son Hui were also included in the entourage.
Many questions remain unanswered, however, including whether the North Koreans have robust enough communication systems to make sure no one panics and launches an attack, said Vipin Narang, an associate professor at the Massachusetts Institute of Technology's Security Studies Program.
North Korea's leader Kim Jong Un inspects an honour guard ahead of his departure to Singapore in Pyongyang June 10, 2018.
In a statement, the White House said Mr Trump would speak to the media before departing for the USA at 8:00pm.
The trip to Singapore - nearly 5,000 kilometers (3,000 miles) south of Pyongyang - represents Kim's farthest trip from home since taking power after his father's death in 2011.
North Korean leaders, who have been subject to some of the world's toughest ever sanctions, have long wanted to meet with the USA president, in part because of the global legitimacy such a summit would provide.More news: USA cuts a deal with Chinese smartphone maker ZTE
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"The entire world is focusing on the historic summit between the DPRK (North Korea) and the USA, and thanks to your honest efforts".
"The senior officials of the party and government sincerely wished Kim Jong Un good successes in the first summit meeting and talks between the DPRK and the U.S. and his safe return", the KCNA said.
Just meeting with Mr. Trump will also give Kim a recognition North Korea has long sought, setting him up as global player and equal to the USA domestically and, internationally, as the leader of a "normal country" worthy of respect.
While fighting a trade war with allies, Trump now brings his America First negotiating style to the deadly topic of North Korea's nuclear weapons.
Even though the big meeting isn't on the schedule until Tuesday in Singapore, there were still plenty of interesting developments over the course of the first full day that President Donald Trump has been in the city.
"If I think it won't happen, I'm not going to waste my time", he said.
Trump's arrival came just hours after Kim, wearing his trademark dark "Mao suit" and distinctive high-cut hairstyle, landed in the ultra-modern city-state on his longest trip overseas as head of state.