This surprise meeting, on the North Korean side of the shared inter-Korean area of Panmunjom, comes after President Trump on Thursday abruptly scuttled a summit with Kim, planned for June 12 in Singapore.
They discussed how to implement the Panmunjom Declaration and the success of a potential Trump-Kim meeting, according to the text from the president's office. He did not confirm how the meeting was arranged or which side asked for it.
The presidential office said Moon will announce the outcome of his second meeting with Kim on Sunday at 10 a.m.
Observers of the soap opera-style Trump-Kim summit drama could be forgiven for thinking that a fragile courtship is underway, where the tenor of each side's statements will determine whether the two can agree to sit down together.
He did not detail the nature of the new US communication with the North.
Pompeo a year ago assembled a working group at the Central Intelligence Agency called the Korea Mission Center, which gradually assumed the lead role in talks with the North Koreans, and the group's director, a retired senior Central Intelligence Agency official with deep experience in the region, became the main USA interlocutor with Pyongyang.
Should the summit take place, it would be the first time for a sitting USA president to meet a DPRK leader. The two countries' leaders had held direct talks just twice before, in 2000 and 2007.
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The close of the program follows with the placing of wreaths, a ceremonial rifle salute and the sounding of "Taps". The VFW Memorial Day Observance is taking place at the same time Monday at the Evergreen Cemetery downtown.
Kim Chang Son, a senior official of North Korea's State Affairs Commission, arrived in Beijing on Thursday, the sources said, adding he may have planned to also visit Singapore to prepare for the recently canceled June 12 summit there.
"The White House pre-advance team for Singapore will leave as scheduled in order to prepare should the summit take place", White House Press Secretary Sarah Sanders said. The delegation was to include White House Deputy Chief of Staff Joseph Hagin and deputy national security adviser Mira Ricardel, US officials said, speaking on condition of anonymity.
In a tweet Friday, the president said his administration is having very productive talks with North Korea about reinstating the meeting.
"We'll see what happens - it could even be the 12th".
"You talk about your nuclear capabilities, but ours are so massive and powerful that I pray to God they will never have to be used", Trump wrote to Kim. They very much want to do it. "We'd like to do it", he said. Trump cited "open hostility" from the North as his reason for backing out.
Kim met Saturday with South Korean President Moon Jae-in, a key figure in brokering the U.S.
Following the meeting, US President Donald Trump announced that he would hold a summit with the North Korean leader in "the coming weeks".
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Before Trump's announcement, Pyongyang had hardened its rhetoric, calling comments by Vice President Mike Pence "ignorant and stupid".
But others said Trump's demonstrated willingness to walk away could yet extract further concessions from Pyongyang.
Moon said Trump's decision left him "perplexed" and was "very regrettable".
The meeting is the latest remarkable chapter in a roller coaster few months on the Korean peninsula.
Dozens of global journalists left North Korea on Saturday after observing the demolition of the underground tunnels in Punggye-ri, where all of the North's six nuclear tests were conducted including its latest and largest in September.
For months, Trump has worked to make the landmark gathering happen. The presidential Blue House did not immediately provide more details.
The White House did not respond to a request for comment. "And if they are ready to do that then. we're certainly ready to have those conversations", she said.
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