Mr Kim, who had to be granted a waiver from sanctions to travel, landed at New York's JFK airport on Wednesday afternoon.
Amid a flurry of diplomatic efforts to salvage a June 12 U.S.
The Trump administration is believed to have granted him a temporary waiver this time to allow him to visit NY, where North Korea has a diplomatic mission to the United Nations.
Trump last week called off the summit after North Korea expressed anger at comments by senior United States officials.
"The conversation is going to be focused on denuclearization of the peninsula", Sanders said.
Dialogue between the two sides began with a dinner meeting held in an apartment building near the United Nations headquarters at 7 p.m., ahead of further talks Thursday to finalize planning for a June 12 summit created to end a nuclear standoff that once threatened to plunge Korea back into war.
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"If it happens, we'll certainly be ready", White House press secretary Sarah Huckabee Sanders said of plans for the summit.
Trump's unpredictability sparked a surprise meeting on Saturday between Kim and South Korean President Moon Jae-in - only the fourth time leaders from the two countries have ever met - as they scrambled to get the talks back on track.
Pompeo and Kim Yong Chol, vice chairman of the ruling Workers' Party's Central Committee, "are trying to get to know each other" following their two initial meetings this year in North Korea, said the US official who asked not to be identified.
Kim Yong Chol was previously chief of the Reconnaissance General Bureau, a top North Korean military intelligence agency, and has spent almost 30 years as a senior member of the intelligence community.
Kim Yong Chol is the highest-level representative from the North to set foot in the United States since 2000.
In a dizzying turnaround less than a week after Trump announced the cancellation of the summit, Kim, the director of North Korea's United Front Department, which is responsible for inter-Korean relations, departed for NY from Beijing Wednesday.
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Such positions, and his omnipresence before and during inter-Korean summits in April and on Saturday, make him one of the most powerful people in North Korea, South Korean officials say.
The US delegation, led by Philippines Ambassador Sung Kim, had been meeting their North Korean counterparts at the Demilitarized Zone since Monday. Trump's letter, the aides said, was created to pressure the North on the global stage for appearing to have cold feet.
White House officials maintain that Trump was hopeful the North was merely negotiating but that he was prepared for the letter to mark the end of the two-month flirtation. Instead, the officials said, it brought both sides to the table with increasing seriousness, as they work through myriad logistical and policy decisions to keep June 12 a viable option for the summit.
Kim Yong Chol is a four-star general, vice chairman of the ruling Workers' Party's Central Committee, and director of the United Front Department, which is responsible for inter-Korean relations.
The White House emphasized that it has remained in close contact with South Korean and Japanese officials as preparations for the talks continue.
Moon has seen how U.S. President Donald Trump "can be cajoled with flattery - he floated the Nobel Peace Prize - and the U.S. president clearly wants the showcase of a summit".
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