Earlier, both Trump and Kim had expressed hope of progress in improving relations and on the key issue of denuclearisation in the Vietnamese capital Hanoi.
White House spokeswoman Sarah Sanders said: “The two leaders discussed various ways to advance denuclearisation and economic driven concepts.
“No agreement was reached at this time, but their respective teams look forward to meeting in the future.”
An earlier White House announcement had said Donald Trump was due to hold a “joint agreement signing ceremony” with Kim Jong-un at the conclusion of the summit talks.
But both leaders left the talks at the Metropole Hotel at around 1.25pm local time (6.25am GMT) and returned to their hotels.
“No agreement was reached at this time, but their respective teams look forward to meeting in the future”
Sarah Sanders, White House spokeswoman
Earlier, the US president and the leader of communist North Korea had seemed confident of progress.
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