According to the State Department, the US team met with North Korean officials at the same DMZ site, the village of Panmunjom.
"We two leaders agreed the June 12 North Korea-US summit must be successfully held", he said.
The White House said Sunday that USA negotiators are in North Korea preparing for a potential meeting with their counterparts.
Now that planned meeting, scheduled for June 12 in Singapore, is off, capping a months-long back-and-forth with nuclear-armed Pyongyang and denying Trump the foreign policy victory he craved.
Mr Trump told reporters at the White House during a meeting with a USA prisoner freed by Venezuela: "It's moving along very nicely".
"Hey Donald, I'm already in Singapore, waiting for you to turn up", Howard X said. It's moving along very nicely.
Speaking at a White House event, the president said the cancellation was a setback for North Korea and the world.
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"I think the two leaders will sit down and they're going to have a great time, because really they have the same personality", he said on Sunday.
He said on Saturday the USA was still considering the 12 June date for the summit in Singapore.
Leading senators from both parties on Sunday scoffed at the notion that Kim would bargain away North Korea's nuclear deterrent, with some warning that his regime may seek significant concessions from the Trump administration in exchange for promises of arms reduction well into the future. So we're looking at June 12th in Singapore. He served as ambassador to South Korea from 2011 to 2014, then became special representative for North Korea Policy, a position that Yun later took over and that is now vacant. But Mr Trump short-circuited that process in March, when he abruptly accepted an invitation to meet with Mr Kim.
According to the USA officials, speaking on condition of anonymity, North Korea has expressed reluctance to ship all of its nuclear weapons and missiles outside the country.
"I told Chairman Kim that if he decides and put into practice a complete denuclearization, President Trump is willing for economic cooperation and ending hostile relations", Moon said. "The biggest challenge is for the global community to jointly prevent North Korea from evading sanctions", Kono told reporters during a visit to Yamagata Prefecture in northeastern Japan.
"This is going to be an opportunity that Japan, which has the abduction issue, should never lose", said Koichi Hagiuda, executive acting secretary general of the ruling Liberal Democratic Party, in a speech in Miyazaki Prefecture, southwestern Japan.
But within 24 hours, he had reversed course, saying it could still go ahead after productive talks were held with North Korean officials.
But Michael Hayden, who served as Central Intelligence Agency director during the George W. Bush administration, said he anxious that Trump might be at a disadvantage in a face-to-face negotiation with Kim.