The meeting comes ahead of a highly-anticipated summit, scheduled for June 12 in Singapore, between Trump and North Korean leader Kim Jong-un.
While Pompeo has traveled twice to North Korea in recent weeks, the meeting will be the highest-level talks between the two sides in the US since 2000, when Vice Marshal Jo Myong Rok flew to Washington to meet with then-President Bill Clinton.
"And a nuclear-capable North Korea with missiles that can reach the United States is unacceptable", Admiral Harry Harris said in a change-of-command speech. Kim is in NY for talks with Secretary of State Mike Pompeo, becoming the most senior North Korean official to visit the U.S. since 2000.
He was to meet US Secretary of State Mike Pompeo, who saw Trump before setting off from Washington, for dinner on Wednesday and talks Thursday to finalize planning for a June 12 summit created to end a nuclear stand-off that once threatened to plunge Korea back into war.
Kim Yong Chol is a powerful surrogate for Kim Jong Un. Pompeo has been an advocate for a Trump-Kim meeting, convinced after his two encounters with the North Korean leader that the regime was genuinely ready to consider dismantling its nuclear program.
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.
The US delegation, led by Philippines Ambassador Sung Kim, had been meeting their North Korean counterparts at the Demilitarized Zone since Monday.
That suggests Kim might have chosen to first go to NY because it would make it easier for him to communicate with officials in Pyongyang, North Korea's capital.
Burgers also have high status in North Korea.
During his tenure as a senior intelligence official, Kim was accused by South Korea of masterminding deadly attacks on a South Korean navy ship and an island in 2010.
The report also details that Kim may offer "limited American investment in North Korea, particularly in infrastructure".
Reporting from New York City, Al Jazeera's James Bays said there is still a "substantial gap" between United States and North Korean positions on the issue of denuclearisation.
The White House emphasized that it has remained in close contact with South Korean and Japanese officials as preparations for the talks continue.