They are likely to cover a wide range of subjects but focus on concrete denuclearization steps the North will take and the USA response, as well as protocol and security at the summit scheduled for February 27-28 in Vietnam.
The document they signed stated that North Korea "commits to work toward complete denuclearisation" but failed to address how and by when it would be achieved.
Ahead of his visit to the Koreas, Bigeun said last week that Kim had committed to "the dismantlement and destruction of North Korea's plutonium and uranium enrichment facilities" during a September summit with Moon and at a meeting with the U.S. secretary of state in October.
These developments have given rise to concerns that the two leaders could settle for the disposal of North Korea's intercontinental ballistic missiles (ICBMs), which the US regards as a direct threat to its national security.
By last autumn, North Korea changed the division in charge of nuclear issues from its foreign ministry to the State Affairs Commission under Kim Jong Un, according to sources knowledgeable about U.S.
On his return to South Korea, Mr Biegun briefed the country's Foreign Minister Kang Kyung-wha. He may surprise some but he won't surprise me, because I have gotten to know him amd fully understand how capable he is.
The three-year conflict ended in an armistice, not a peace treaty, leaving the two Koreas still technically at war, with the United States keeping 28,500 troops in the South.
"Our discussions were productive", Mr Biegun, said while meeting Ms Kang.
The President also appeared to reference his previous mocking of Mr Kim as the "Little Rocket Man".
He also said his talks in North Korea had been productive, but admitted more "hard work" was required before the summit.
The anniversary is a holiday in North Korea.
Palladino said the location of the summit in Vietnam will be disclosed when it's ready for announcement.
The summit will focus on fleshing out the North's concrete steps for the "complete denuclearization" of the peninsula that Trump and Kim agreed to in their first encounter in Singapore last June, and what the U.S. can offer in exchange for them.
"I am confident that if both sides stay committed, we can make real progress", he said.
In addition to concrete denuclearization measures, Washington is believed to be demanding the regime to dismantle all of its missiles, including its medium and short-range projectiles.
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