Who is Gen Kim Yong-chol?
The official said that broadly, the "goal is denuclearization".
The rivals also agreed at a meeting of senior officials at the border village of Panmunjom to establish a liaison office at the North Korean border town of Kaesong and hold sports talks on fielding combined teams for some sports at the Asian Games in August, as they continue to take steps toward reconciliation.
The historic meeting between Mr Trump and Kim Jong-un would be the first between sitting United States and North Korean leaders.
Within a day, both sides were in new talks to save the summit, and Kim Yong-chol flew to NY this week to meet Secretary of State Mike Pompeo.
This photo, taken by the Joint Press Corps on June 1, 2018, shows South Korea's chief delegate Cho Myoung-gyon (right) and his North Korean counterpart Ri Son-gwon entering to hold inter-Korean high-level talks. The president even said he's contemplating two or three meetings with Kim Jong Un if everything goes well and there is more progress to be made.
Amid all these things, Lavrov added an air of mystery to the meeting by presenting Kim Jong-un with a mysterious box, leaving everyone guessing about its contents, as per a report from Russia Today. "It is very important to them". "I think we're looking for something that has never been done before". It is all a process.
The key meeting, scheduled for 12 June, has been jeopardised so far by belligerent statements from North Korea and threats of cancellation from Mr Trump. Maybe you have to have a second or a third.
North Korea's envoy Kim Yong Chol (left) shakes hands with US Secretary of State Mike Pompeo during their meeting in New York, US.
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But Kim Jong Un, in a meeting with Russia's foreign minister on Thursday, complained about "U.S. hegemonism", a comment that may complicate the summit plans. It was not clear whether the United States president would receive Kim Jong-un's envoy in the Oval Office.
The meeting is remarkable as it is the Trump administration's first taste of the Kim regime unfiltered by mediators like South Korea.
They are trying to hash out sharply differing ideas of denuclearizing North Korea.
It is still not clear whether North Korea's vision of "denuclearisation" in exchange for security guarantees and sanctions relief can be brought into line with Washington's demand for a "complete, verifiable and irreversible" end to its nuclear programme.
Earlier in the day, Trump told reporters in Washington that Pompeo's meetings with Kim, North Korea's former military intelligence chief whom the State Department describes as Kim Jong-un's "point person", had been going "very well".
"The potential summit between @POTUS and Chairman Kim presents #DPRK with a great opportunity to achieve security and economic prosperity", Pompeo tweeted shortly before the meeting began.
Trump sent a letter last week to Kim Jong Un, calling off the June 12 summit. The days since have seen a flurry of diplomatic efforts to get the summit back on track.
"I am confident we are moving in the right direction", Pompeo told reporters at a news conference in NY after meeting Thursday with former North Korean military intelligence chief Kim Yong-chol.