Secretary of State Mike Pompeo clinks glasses full of Islay Scotch with North Korean general Kim Yong Chol at a dinner in NY on May 30, 2018. But North Korea flipped on the U.S. in May, blasting Trump officials and saying it was reconsidering the summit.
After the meetings, Mr Pompeo told a media conference on Friday morning (AEST) it would be "tragic to let this opportunity go to waste" with North Korea.
The U.S. insists that North Korea must give up all its nuclear weapons before it can shed its pariah status or get any relief from a crushing sanctions regime.
"As we move to adjust to the political situation in the face of U.S. hegemonism, I am willing to exchange detailed and in-depth opinions with your leadership and hope to do so moving forward", he said.
"As we move to adjust to the political situation in the face of United States hegemonism, I am willing to exchange detailed and in-depth opinions with your leadership and hope to do so moving forward", he told Mr Lavrov. "The meetings have been very positive".
On the possibility of a quick solution to the crisis, Trump said today as he was boarding Air Force One: "I'd like to see it done in one meeting".
Moon, who has lobbied hard for nuclear negotiations between Trump and Kim Jong Un, held a surprise meeting with the North Korean leader on Saturday in an effort to keep the summit alive.
Russian Foreign Minister Sergei Lavrov in Pyongyang on Thursday invited North Korean leader Kim Jong Un to visit Russia, Moscow said, during the first meeting between the head of the reclusive state and a Russian official.
North Korea has strongly objected to statements by Trump administration members comparing North Korean denuclearisation to Libya's. It's the highest-level meeting between a U.S. president and a North Korean official since 2000.
US Secretary of State Mike Pompeo (2nd L) holds talks with North Korean envoy Kim Yong-chol (2nd R) in NY, on May 31, 2018.
U.S. officials now expect the summit to go ahead, but they want North Korea to accept that nuclear disarmament be at the heart of the discussion - and warn that there can be no end to trade sanctions without it.
"The conditions are putting President Trump and Chairman Kim Jong Un in a place where we think there could be real progress made by the two of them meeting", he said.
He is the vice chairman of the central committee of the Workers' Party of Korea.
In 2016, he took charge of the United Front Department, the civilian intelligence agency which supposedly operates pro-North Korean groups in South Korea and handles inter-Korean affairs.
The State Department released photos of a smiling Pompeo shaking hands with Kim Yong Chol, pointing out NY landmarks to him by a window and toasting his guests.
However, officials both sides have since said they are still working toward making the June 12 meeting happen.
He also expressed Moscow's support for an agreement Mr Kim reached with South Korea at a summit last month that focused on measures to ease hostilities and increase exchanges between the two Koreas. The White House said the were scheduled to have a full day of talks on Thursday.
Kim Yong-chol, vice chairman of the North Korean ruling party's central committee, was allowed into the United States despite being on a US sanctions list, and North Korean officials are not normally allowed to travel outside the NY area.
During his tenure as a senior intelligence official, Kim was accused by South Korea of masterminding deadly attacks on a South Korean warship and an island in 2010. Trump had called it off last week in response to threatening rhetoric from the DPRK.