Kim may see a meeting with Trump as necessary to easing pressure from crushing sanctions and to winning security assurances in a region surrounded by enemies.
Nauert provided no further details.
Sung Kim had been on standby in Seoul since last week. Allison Hooker, a Korea specialist on the National Security Council, is reportedly also part of the team. While the high-stakes meeting may proceed as planned, experts say it's unlikely to live up to the hype as ambiguity remains about the definition of denuclearization and whether the USA can convince the Kim regime that it can remain in power after giving up its weapons.
But as the clock ticks toward June 12, Trump's aides are describing a renewed sense of urgency to make progress that would allow the two leaders to meet on schedule.
"A lot of people are working on it", Trump said.
"I think the two leaders will sit down and they're going to have a great time, because really they have the same personality", said Howard on Sunday.
It has long said it is open to eventually giving up its nuclear arsenal if the United States withdraws its troops from South Korea and ends its "nuclear umbrella" alliance with Seoul. Another U.S. delegation was in Singapore to work on logistics.
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The meeting was the latest dramatic turn in a week of diplomatic ups and downs surrounding the prospects for an unprecedented summit between the United States and North Korea, and the strongest sign yet that the leaders of the two Koreas are trying to keep the on-again off-again meeting on track.
Any attendance by Mr Moon would be dependent on the progress of pre-summit talks between the USA and North Korean leaders, said the Blue House.
More significantly, Moon secured the restart of minister-level inter-Korean talks on June 1, followed by a dialogue between military leaders and a Red Cross meeting to reunite families separated by the war.
The second meeting between Kim and Moon in as many months reflects urgency among both men to maintain momentum for diplomacy. But experts are hardly optimistic about a breakthrough, even if the meeting goes ahead.
Trump announced on Sunday over Twitter that meetings between Americans and North Koreans were being held on the northern side of the inter-Korean truce village of Panmunjom, raising hopes for the resurrection of the summit. South Korea and China account for nearly all of North Korea's land borders, so their support is essential for enforcing sanctions ramped up past year after Mr Kim declared the ability to strike the United States with a nuclear weapon.
While China's government publication claims North Korea came out looking better from its insulting approach to the United States than the trump administration, the Global Times lamented that it was possible that North Korea's change in tone following the first cancelation of the summit "may encourage the White House's obsession with its hard-line approach".
Trump said Sunday that a US team was in North Korea to work on plans.
Until this point, it's been unclear whether Kim is willing to agree to a timetable for abandoning his nuclear weapons program and what demands he will have for the United States in return.
"Ultimately, I remain convinced that he does not want to denuclearize - in fact, he will not denuclearize".
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