– A team of U.S. officials crossed into North Korea on Sunday for talks to prepare for a summit between President Donald Trump and Kim Jong Un, as both sides press ahead with arrangements despite the question marks hanging over the meeting.

Sung Kim, a former U.S. ambassador to South Korea and former nuclear negotiator with the North, has been called in from his post as envoy to the Philippines to lead the preparations, according to a person familiar with the arrangements.

The talks are focused on what would be the substance of a summit between Trump and Kim — the issue of North Korea’s nuclear weapons.

After Saturday’s surprise inter-Korean talks, South Korean President Moon Jae-in said Kim was still committed to the “complete denuclearization” of the Korean Peninsula. But Moon declined to define “complete denuclearization,” suggesting that there are still fundamental gaps on the key issue bedeviling preparations.

Crossing the line that separates the two Koreas, Sung Kim met with Choe Son Hui, the North Korean vice foreign minister, who said last week that Pyongyang was “reconsidering” the talks. The two officials know each other well — both were part of their respective delegations that negotiated the 2005 denuclearization agreement through the six-party framework.

The meetings were trumpeted by Trump later Sunday afternoon when he tweeted, “Our United States team has arrived in North Korea to make arrangements for the Summit between Kim Jong Un and myself. I truly believe North Korea has brilliant potential and will be a great economic and financial Nation one day. Kim Jong Un agrees with me on this. It will happen!”

The talks are expected to continue Monday and Tuesday at Tongilgak, or “Unification House,” the building in the northern part of the Demilitarized Zone where Kim Jong Un met Moon on Saturday. That impromptu session was aimed at salvaging the summit that Trump had said he was scrubbing just two days earlier.

The South Korean leader, who is playing an informal mediator role, was optimistic afterward. “We two leaders agreed the June 12 North Korea-U.S. summit must be successfully held,” he said.

In Washington, lawmakers and former U.S. intelligence officials expressed general support Sunday for proceeding, but many reacted skeptically to North Korea’s suggestion that it is open to discussing denuclearization.

“They’re playing a game,” Sen. Marco Rubio, R-Fla., 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 denuclearize. I just, I’m not very optimistic about that.”

James Clapper, the former director of national intelligence and a onetime senior intelligence officer for U.S. forces in South Korea, said he worried that North Korea’s idea of “denuclearization” entails scaling back or eliminating U.S. strategic forces in the Pacific.

Clapper suggested that a worthy goal might be to establish a “regular conduit for communication” between the two nations, perhaps including the opening of diplomatic interest sections in both capitals.

“This is not a reward for bad behavior at all,” Clapper said on CBS. “It’s mutually reciprocal and would give us that presence there, more insight and more understanding.”

Michael Hayden, the CIA director during the George W. Bush administration, said he worries that Trump might be at a disadvantage in a face-to-face negotiation with Kim.

“I don’t know the president has done the kind of homework that would allow him to do this,” Hayden said on Fox. Hayden said the “real danger” is not the rhetoric and theatrics, but rather, the substance: “What will happen at this meeting?”

“These folks are not going to get rid of all their nuclear weapons,” Hayden said. “And if President Trump’s brand — and that’s the right word here, 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 the administration had enlisted Sung Kim 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 the Massachusetts Institute of Technology, noting that the summit preparation was best handled by experts behind the scenes rather than in public forums such as Twitter.

Sung Kim, who was born in South Korea and was a key diplomat in the 2005 six-party talks, 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.