The meetings are expected to continue tomorrow and Wednesday at Tongilgak, or "Unification House," the building in the northern part of the DMZ where Kim Jong Un met South Korean President Moon Jae In yesterday for impromptu talks aimed at salvaging the summit, scheduled to be held in Singapore.
The two delegations are focused on the substance of any summit between the Trump and Kim Jong Un: the issue of North Korea's nuclear weapons programme.
After the surprise inter-Korean talks, South Korean President Moon Jae In said Kim was still committed to the "complete denuclearisation" of the Korean Peninsula. But Moon declined to define "complete denuclearisation," suggesting that there are still fundamental gaps on the key issue bedeviling preparations.
The South Korean President, who is playing something of a mediator role in the talks, was optimistic after his meeting at the weekend, his second in a month with Kim. "We two leaders agreed the June 12 North Korea-US summit must be successfully held," he said.
In Washington, lawmakers and former US intelligence officials expressed general support for proceeding with the summit, but many reacted sceptically to North Korea's suggestion that it is open to discussing denuclearisation.
"They're playing a game," Senator Marco Rubio, (R), a member of the Senate Foreign Relations Committee, said on CBS. "Kim Jong Un - these nuclear weapons are something he's psychologically attached to. They are what give him his prestige and importance. … I'd love to see them denuclearise. I just I'm not very optimistic about that."
James Clapper, the former director of national intelligence and a one-time senior intelligence officer for US forces in South Korea, said he was worried that Trump may be opening himself to demands that the United States scale back its own strategic forces in the Pacific.
"When we say 'denuclearisation of the Korean Peninsula,' this could be a two-way street," Clapper told CBS
Clapper suggested that a worthy goal for the summit might be to establish a "regular conduit for communication" between the two countries, perhaps including the opening of diplomatic interest sections in both capitals.
But Michael Hayden, the CIA director during the George W. Bush Administration, said he was worried that Trump might be at a disadvantage in any a face-to-face negotiation with Kim. While the North Korean side will likely be fully prepared for the summit, "I don't know the President has done the kind of homework that would allow him to do this," Hayden told Fox News.
"Therein lies the real danger: It's what will happen at this meeting," Hayden said. "These folks are not going to get rid of all of their nuclear weapons, and if President Trump's brand … going into this meeting demands something like that, this is going to end up in a very bad place."
Given all the ups and downs with the summit, many analysts were relieved to hear that Sung Kim had been enlisted to help, especially given the retirement of fellow seasoned diplomat Joseph Yun earlier this year.
"This is a great step," said Vipin Narang, a nuclear nonproliferation expert at MIT, noting that the summit preparation was best handled by experts behind the scenes rather than in public forums like Twitter.
"This is how progress is made, and the best chance to have a summit, and one that yields meaningful outcomes," Narang said.
Sung Kim, who was born in South Korea, was a key diplomat in the 2005 six-party talks. 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.
His North Korean counterpart, Choe, also has years of experience working on these issues and is well connected within the North Korean hierarchy.
She has also served as a nuclear negotiator and led the US affairs division in the North Korean Foreign Ministry until being promoted to vice foreign minister this year. The daughter of a former premier, she is also thought to have direct access to Kim Jong Un.
Most analysts still thinks it is extremely unlikely that North Korea will surrender its nuclear weapons.
Still, it might be able to narrow the gap. "This is an opportunity to find out what, in fact, they might be willing to do and vice versa - and that is the most important step right now," Narang said.
