"We've got a very interesting meeting in particular tomorrow, and I just think it's going to work out very nicely", Trump told Singapore's Prime Minister Lee Hsien Loong during their talks, according to a pool report.
Singapore's Prime Minister Lee Hsien Loong and North Korean leader Kim Jong-un have discussed bilateral relations and the situation on the Korean Peninsula, the city-state's Foreign Ministry said in a statement.
On his way to Asia from the G7 meeting in Canada, Trump said he was embarking on a "mission of peace", predicting he'll know "within the first minute" if Kim is serious about negotiating.
One dispatch by the Korean Central News Agency said North Korea and the USA would exchange "wide-ranging and profound views" on establishing new relations, building a "permanent and durable peace-keeping mechanism", achieving denuclearization and "other issues of mutual concern, as required by the changed era".
It was reported last month that South Korean President Moon Jae-in might join in the talks between Kim and Trump if their summit in Singapore proves successful.
"Welcomed Chairman Kim Jong-Un, who has just arrived in Singapore", Balakrishnan tweeted.
The Rodong Sinmun newspaper, the mouthpiece of the ruling Workers' Party, devoted its first two pages and 16 photos to Kim's trip, including images of him boarding an Air China Boeing 747 for the journey.
Kim's summit with Trump has captured intense global attention after a turn to diplomacy in recent months after serious fears of war previous year amid North Korean nuclear and missile tests.
"I am on my way to Singapore where we have a chance to achieve a truly wonderful result for North Korea and the World", Trump wrote in a pair of tweets.
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USA presidents and vice-presidents generally never fly on the same aircraft to guarantee that one of them survives in the event of a disaster, and the move appeared created to ensure the preservation of the Kim dynasty, which has ruled the North for three generations.
"It's never been done before", Trump said of a U.S.
The US president was accompanied by Secretary of State Mike Pompeo, National Security Adviser John Bolton, White House Press Secretary Sarah Sanders and White House Chief of Staff John Kelly.
The talks have been portrayed by Trump in recent days more as a get-to-know-you session.
On Wednesday, the summit was declared an "Enhanced Security Special Event" by the Minister for Home Affairs under the Public Order Act.
But many, if not all analysts, say that this is highly unlikely, given how hard it has been for Kim to build his program and that the weapons are seen as the only protection he has. He has also raised the possibility of further summits and an agreement ending the Korea War by replacing the armistice signed in 1953 with a peace treaty. Any deal would likely depend on North Korea's willingness to open its facilities for inspection. China and South Korea would have to sign off on any legal treaty.
North Korea wants a staged approach to dismantling its nuclear weapons program and a security guarantee from the United States in return.
Trump and other top US officials have promised a "bright future" for the North if it quickly relinquishes its nuclear weapons - including economic inducements and a security agreement. Progress could lead to a peace treaty and formally end a state of war on the Korean Peninsula, which has persisted for almost 70 years.