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 U.S. in the lead-up to the talks. The U.S. wants a complete, "irreversible" and "verifiable" dismantling of North Korea's nuclear sites.
That meeting looked uncertain last week, after a turbulent few days of diplomatic brinkmanship that culminated in a letter by Trump to Kim, saying he would abandon the summit because of Pyongyang's "open hostility" towards US Vice President Mike Pence.
Scheduled to happen in Singapore, a bilateral between Mr Trump and Mr Kim would be the first between sitting United States and North Korean leaders.
"Our secretary of state is having very good meetings".
The meeting between Pompeo and Kim Yong Chol is particularly significant because of the degree of influence the North Korean general, a former intelligence official with a controversial history in charge of the regime's relations with South Korea, enjoys with the country's leader.
Mr Trump cancelled the 12 June summit, but both sides agreed to move forward.
Kim Yong Chol is the highest-ranking North Korean official to visit the United States in 18 years.
Kim said he hoped to find a "solution to meet the interests of each other through a new method in a new era and under a new situation and the solution of the issues will progress through effective and constructive dialogue and negotiation", the official Korean Central News Agency said.
His comments will stoke fears that the tempestuous relationship between Mr Trump and North Korean leader Kim Jong Un could yet spiral into World War 3.
"North Koreans have defined what they want as security, and they have determined some years ago that security could be found with nuclear weapons", said the official.
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Gen Kim has previously served as chief of Pyongyang's top military intelligence agency, and was sanctioned twice by US and South Korea for his role in supporting North Korea's nuclear and missile programme in 2010 and 2016.
"We've had lots of conversations around that", he said.
North Korea's flurry of diplomatic activity following a torrid run in nuclear weapons and missile tests in 2017 suggests that Kim is eager for sanctions relief to build his economy and the worldwide legitimacy the summit with Trump would provide.
Neither Kim nor Pompeo acknowledged questions from reporters as they met in a senior U.S. diplomat's apartment in the Corinthian, a luxury high-rise condo with a dramatic view over United Nations headquarters and mid-town Manhattan.
He is North Korea's former military intelligence chief and is one of the North Korean leader's closest aides.
The letter comes as the two countries work to revive a Trump-Kim summit on June 12 in Singapore.
Mr Trump tweeted this morning: "Very good meetings with North Korea".
He admitted that he still could not confirm whether the summit will go ahead.
Seoul's unification minister Cho Myoung-gyon told reporters before the meeting: "We will hold discussions with the North so that we can implement the agreements between the two leaders with pace and without hitches and also create a positive atmosphere for the leaders' summit between North Korea and the United States". Trump had called it off last week in response to threatening rhetoric from the DPRK.