U.S. intelligence says the North Koreans have started pulling cables from the tunnels at their nuclear test site -- a first step toward closing them down, CBS News' national security correspondent David Martin reports. North Korean leader Kim Jong Un has vowed to shut down the country's nuclear test site in May, Seoul's presidential office said on Sunday.

Kim had made the comments during his summit with South Korean President Moon Jae-in on Friday at a border truce village. The leaders of the two countries met Friday for the first time since 1953.

Kim and Moon during the summit promised to work toward the "complete denuclearization" of the Korean Peninsula, though they did not mention specific plans or timetables. They also agreed to work toward formally ending the 1950-53 Korean War and push for three-way talks with Washington or four-way talks that also include Beijing to do so.

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The Koreas can't officially end the war themselves because South Korea wasn't a direct signatory to the armistice that stopped the fighting but left the peninsula technically in a state of war.

More substantial discussions on the North's denuclearization -- including what, when and how it would occur -- are expected between Kim and President Donald Trump, who could meet in May or June. On Monday, Mr. Trump suggested the Korean Demilitarized Zone could be a possible option to host the eventual talks, calling it an "intriguing" choice.

His comments, which took place at a joint press conference with Nigerian President Muhammadu Buhari, followed a tweet early Monday in which he said the "Peace House/Freedom House, on the Border of North & South Korea" could possibly host the summit.

"Some people don't like the look of that, some people like that very much," said Mr. Trump in the Rose Garden on Monday. He added, "There's something I like about it because you're there, you're actually there where if things work out there's a great celebration to be had on the site not in a third party country."

"The good news is, everybody wants us. It has the chance to be a big event," he suggested.

Mr. Trump added, "personally I think it's going to be a success." "If its not a success, I will respectfully leave," he said.

The president also said that Kim has been "very open and very straightforward so far" in discussing the possibility of removing nuclear testing sites and halting the launching of ballistic missiles.

While the Kim-Trump talks is shaping up to be crucial, there's still widespread doubt whether Kim will ever agree to entirely abandon his nuclear weapons when he apparently sees them as providing his only guarantee of survival in a region surrounded by enemies.

Seoul has said Kim expressed genuine interest in dealing away his nuclear weapons. But North Korea for decades has been pushing a concept of "denuclearization" that bears no resemblance to the American definition, vowing to pursue nuclear development unless Washington removes its troops and the nuclear umbrella defending South Korea and Japan.

On Wednesday, China's foreign minister arrived in North Korea's capital and could meet with Kim while trying to ensure a larger role for Beijing in the new round of nuclear diplomacy with Pyongyang that has been driven by Seoul and Washington. Wang is likely to use his visit to further ensure that Beijing would not be sidelined in the high-stakes discussions surrounding the North. Some South Korean analysts believe Wang would specifically seek Kim's commitment that the process on formally ending the war would include China.