Coming after a surprise meeting between Kim and South Korean President Moon Jae-in, the move was the latest sign that the on-again, off-again Trump-Kim summit may yet go ahead as planned.
At their first meeting on April 27, Moon and Kim agreed to pursue "complete" denuclearization of the Korean Peninsula and to work toward a formal end to the 1950-1953 Korean War.
Moon, who returned to Seoul on Thursday morning after meeting Trump in Washington earlier this week in a bid to keep the summit on track as initially planned, for June 12 in Singapore, was due to announce details of the meeting with Kim early on Sunday.
Success in talks would be a huge accomplishment for Mr Trump, while meeting with the U.S. president as an equal on the world stage would be a major coup for Mr Kim.
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.
Video footage also showed Kim Jong Un's sister, Kim Yo Jong, greeting Moon as he arrived at Tongilgak and shaking hands, before the South Korean leader entered the building flanked by North Korean military guards.
Should the summit take place, it would be the first time for a sitting US president to meet a DPRK leader.
The leaders held talks for two hours in the same Panmunjom truce village where they had met last month, making a declaration vowing to improve ties.
Trump welcomed the North's conciliatory response to his Thursday letter withdrawing from the June 12 meeting in Singapore with Kim Jong Un.
The North's decision to close the Punggye-ri nuclear test site has generally been seen as a welcome gesture by Mr Kim to set a positive tone ahead of the summit.
Koh Yu-hwan, am expert on Korean relations at Dongguk University, said Saturday's meeting between Moon and Kim increased the likelihood of the Singapore summit taking place as originally intended.
The original decision to abandon the historic summit blindsided South Korea which had brokered a remarkable detente between Washington and Pyongyang after months of Kim and Trump trading insults and threats of war.
Earlier on Friday, speaking to reporters outside the White House in Washington, the U.S. president indicated that the summit could still be salvaged, saying: "We're gonna see what happens".
"We'll see what happens - it could even be the 12th". "The US called off the summit, so the Chinese probably feel they've done what they can". "We would like to do it", Trump said, and "they very much like to do it". "We'd like to do it", he said.
Reporters were not notified of the summit beforehand and it was only attended by the two Koreas' incumbent and former spymasters: South Korea's National Intelligence Service Director Suh-hoon and Kim Young-chul, former chief of the North's Reconnaissance General Bureau. The person, who asked not to be identified discussing internal matters, said the "maximum pressure" campaign to strangle North Korea's economy is working, and Kim's regime will have to come to the table eventually.
Elms explains that "the use of the term "Libya" and repeated discussions about unilateral disarmament are very hard kind of language to use before you've even had the opportunity to sit down and meet for the first time".
Trump later tweeted that the two countries were "having very productive talks".