Simultaneously, Kim met Russia's Foreign Minister Sergei Lavrov and, according to official news agency KCNA, said the North's "will for denuclearisation of the Korean peninsula still remains unchanged and consistent and fixed".
After the North's combative statements, there was debate inside the Trump administration about whether it marked a real turn to belligerence or a feint to see how far Kim Jong-un could push the United States in the lead-up to the talks.
Pompeo said that after a series of meetings he believes the talks are going in "the right direction".
Pyongyang is seeking worldwide recognition and security guarantees and it is far from clear whether its own vision of the "denuclearisation" of the Korean peninsula can be brought in line with Washington's.
"It is clear that the process of rapprochement between the United States and the DPRK and their abandonment of hostility and mistrust in relations, without which any lasting agreements are impossible, will take a long time and will necessitate well-calibrated moves to meet each other halfway", said the senior diplomat.
After his second summit with Kim on May 26, Moon voiced hopes that should the Trump-Kim summit succeed, the leaders of the two Koreas and the USA could push for a declaration of a formal end to the war. -North Korea meetings, "South Korea and the United States have been in consultation almost daily through many phone calls between Foreign Minister Kang Kyung-wha and Secretary of State Pompeo, as well as through diverse diplomatic channels at various levels". Trump, after this letter, expressed willingness to put the June 12 summit back on track.
North Korean envoy Kim Yong Chol arrives to meet with U.S. Secretary of State Mike Pompeo for talks on nuclear disarmament on Thursday in New York City. Trump's letter, the aides said, was created to pressure the North on the worldwide stage for appearing to have cold feet.
Sanders added that there are other meetings with North Korean officials taking place in Singapore and Korea.
Secretary of State Mike Pompeo held a press briefing in New York Thursday after meeting with Kim Yong Chol, the vice chairman of North Korea.
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Privately, there is increasing acknowledgment in the administration that any disarmament will not be immediate but could take years, and will require United States concessions along the way - a step-by-step process that some senior White House aides have previously rejected, citing North Korea's history of reneging on its promises.
But he said that, after what has now been two meetings with Kim Jong Un and three with Kim Yong Chol, he believes the North is at least ready to consider meeting U.S. demands for denuclearisation.
Kim Yong-chol, vice chairman of the North Korean ruling party's central committee, was allowed into the United States despite being on a USA sanctions list, and North Korean officials are not normally allowed to travel outside the NY area.
Washington would need "action" and "commitment" from the North, and in turn, the official said, offering a "brighter future for North Korea if it makes a smart choice".
In Moscow, Kremlin spokesman Dmitry Peskov said it was too early to know whether there would be a Putin-Kim meeting in Russian Federation.
A senior US State Department official briefed reporters separately as Pompeo and Kim Yong Chol met late on Wednesday.
The summit would discuss ways of denuclearising the Korean peninsula, building on a historic North-South Korea summit in April.
The meeting follows two landmark summits between the leaders of North and South Korea in the last five weeks. Trump hosted South Korean President Moon Jae-in last week.