"It was all about the sanctions," Mr Trump told reporters. "They wanted the sanctions lifted in their entirety and we couldn't do that."
The pair had been expected to announce progress on denuclearisation.
"Sometimes you have to walk and this was one of those times," Mr Trump said.
Speaking at a news conference after the summit, in the Vietnamese capital, Hanoi, Mr Trump said no plans had been made for a third summit.
The original White House programme for the day had planned for a "joint agreement signing ceremony" as well as a working lunch for the two leaders, but expectations were abruptly dashed with the cancellation of both.
What were the sticking points?
According to Mr Trump, Mr Kim made a significant offer - to dismantle all of the Yongbyon complex, the research and production facility at the heart of North Korea's nuclear programme. But in return Mr Kim wanted all sanctions on North Korea lifted, something the US was not prepared to offer.
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