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5 year oldThey shook hands for the media before holding talks and having dinner at the five-star Metropole hotel.
They are expected to discuss a roadmap for ridding the Korean peninsula of nuclear weapons in two days of talks.
There has been little progress on that and other issues since the first Trump-Kim summit in Singapore last year.
Mr Trump said he thought this latest meeting would be "very successful". He denied he was "walking back" on denuclearisation. Asked whether a formal end to the Korean War might be declared, he said: "We'll see."
He said he looked forward to helping Mr Kim achieve a "tremendous" economic future for his country.
Mr Kim, whom the US president described as a "great leader", said he was confident there would be an "excellent outcome that everyone welcomes".
"I'll do my best to make it happen," he told reporters, before the men sat down to eat.
According to the Washington Post, four journalists were banned from attending the dinner - they reported for Bloomberg News, the LA Times, and the Associated Press and Reuters news agencies.
White House press secretary Sarah Sanders said the number of journalists had been limited "due to the sensitive nature of the meetings".
Earlier, Mr Trump tweeted in praise of the host country, writing: "Vietnam is thriving like few places on earth. North Korea would be the same, and very quickly, if it would denuclearize."
"The potential is AWESOME," he added.