The results of this week's parallel talks are likely to dictate whether the June 12 summit between Trump and Kim is possible, according to a USA official familiar with the ongoing deliberations.
South Korean newspaper Segye Ilbo reported Tuesday Kim was seen accompanied by Choe Kang Il, North Korean deputy chief for North American affairs.
To address the North's security concerns, U.S. Secretary of State Mike Pompeo has said that Washington would seek security assurances for Pyongyang "in the same way we are demanding a permanent, irreversible denuclearization".
On a separate but complementary track was the CIA team Pompeo set up past year when he headed the spy agency.
Randall G. Schriver, the assistant secretary of Defense for Asian and Pacific Security Affairs, and Allison Hooker, director for Korea on the White House's National Security Council, were also part of the USA delegation that traveled to North Korea.
On Monday, veteran American diplomat Sung Kim led an American delegation to Panmunjom at the demilitarised zone (DMZ) for talks with North Korean officials.
The Korean leaders' second summit in a month saw bear hugs and broad smiles.
South Korea's presidential palace refused to confirm any details of the latest inter-Korean summit, saying President Moon himself will explain the outcome in a press conference on Sunday.
"So the key issue in the bilateral negotiations will be to what extent the North would accede to the USA demand", he added.
The United States now has no ambassador to South Korea, even as it takes up one of the most delicate diplomatic challenges in years.
Trump views a summit as a legacy-defining opportunity to make the nuclear deal that has evaded others, but he pledged to walk away from the meeting if he believed the North wasn't serious about discussing dismantling its nuclear program.More news: ‘I’m alive’: Russian reporter, Ukraine police faked killing
The first Moon-Kim summit was held on the South Korean side of Panmunjom on April 27.
Trump earlier said his country too was talking to North Korea about their summit.
Victor Cha, who was President George W. Bush's top advisor on North Korea and was briefly expected to get Trump's nod as ambassador to South Korea, said Sunday he was now confident the summit will take place.
And President Trump said over the weekend that we're doing very well in terms of the summit with North Korea.
The meeting, led by White House Deputy Chief of Staff for Operations Joe Hagin on the US side and director of department at the State Affairs Commission and Kim Jong Un's chief secretary Kim Chang Son on the DPRK side, will reportedly discuss "practical issues" surrounding the planned summit in Singapore in talks on Tuesday. Sung Kim, the former USA ambassador to South Korea and current ambassador to the Philippines, led that American delegation, an American official told Reuters.
They agreed to have their top officials meet again June 1.
He said his surprise meeting with Kim came at a suggestion from the North Korean leader, who on Friday expressed hope to meet for candid dialogue.
INSKEEP: So who is this official Kim Yong Chol? Kim Young Chol, the vice- chairman of North Korea, heading now to NY. The North hasn't openly repeated those same demands after Kim's sudden outreach to Seoul and Washington.
"But to achieve the complete denuclearization (of the North) may take more time than expected", he added, pointing to a complicated disarmament process that may call for the dismantlement of Pyongyang's "past, present and future" nuclear arms.
Before he canceled the summit, Trump did not rule out an incremental approach that would provide incentives along the way to the North.
While there have been a few instances in which countries were persuaded to abandon their nuclear ambitions in exchange for sanctions relief and compensation, none of the cases are directly applicable to North Korea, which has advanced its nukes further and with greater zeal than any of the others.