North Korea's position going into the meetings with Pompeo was that a pledge of denuclearization alone should open the way to economic relief, said the official who briefed reporters earlier on Wednesday and spoke on condition of anonymity.
But continuing differences between the two countries led Mr. Trump to abruptly cancel the planned summit last week, and then quickly announce that it might still be held as scheduled on June 12.
A "pre-advance" team of USA officials has also traveled to Singapore to meet with North Koreans there, the White House said.
The Trump administration needed to issue a waiver for Gen. Kim to travel to NY, after the Obama administration in 2010 placed sanctions on him in his role as head of North Korea's premier intelligence agency, the Reconnaissance General Bureau.
Kim, the most senior North Korean official to visit the USA in 18 years, was seen exiting the Corinthian building in Manhattan at around 8.30 p.m., following a dinner with Pompeo, America's chief diplomat. "That is how you do these things".
A senior State Department official said the goal of the meeting was to seek a broad agreement on what a successful summit might look like just two weeks from now. The two also clinked glasses full of whiskey, as a photo shared on Pompeo's official Twitter account showed, which Kim Yong Chol no doubt appreciated as he has been described as a "heavy drinker" by one of the South Korean musicians who performed in Pyongyang in April.
Trump hits Canadian steel, aluminum with tariffs
The move has angered the European Union as well as Mexico, who have threatened to retaliate against the United States measure. The move will likely trigger serious retaliation from the three countries and push the USA to the edge of a trade war.
Separately on Wednesday at Pearl Harbor in Hawaii, Admiral Harry Harris, the outgoing head of US Pacific Command who is Trump's pick to be the ambassador to South Korea, said North Korea remained the United States' most imminent threat. "The secretary of state is from the heartland and likes American food, and he's hosting someone who's never been to our country", the official said.
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North Korea denied any involvement in the attack on the ship and on Sony Pictures.
The administration is arguing that if the North Koreans want security, it can not come from nuclear weapons. He also expressed Moscow's support for an agreement Kim reached with Moon at a summit last month that focused on measures to ease hostilities and increase exchanges between the two Koreas.
North Korea's flurry of diplomatic activity following a torrid run in nuclear weapons and missile tests in 2017 suggests that Kim Jong Un is eager for sanctions relief to build his economy and the global legitimacy the summit with Trump would provide.
Lavrov's May 31 visit - his first to North Korea since 2009 - was seen as an attempt by Moscow to ensure its voice is heard in Pyongyang's diplomatic overtures with the United States and South Korea. "It will not be easy to narrow the gap and find common ground but I think it would not be impossible". "We'll certainly be prepared if it for some reason takes place at a later date".
"The readout from these meetings has been positive", Sanders said.