The right-hand man to North Korean leader Kim Jong-un and US Secretary of State Mike Pompeo have concluded two days of talks in New York.
Gen Kim Yong-chol flew from China on Wednesday to discuss a historic summit between the two nation's leaders.
He is the most senior North Korean to visit the US in nearly 20 years.
US President Donald Trump has told reporters he expects Gen Kim to come to Washington DC on Friday and deliver a letter from Kim Jong-un.
Speaking aboard Air Force One on his way to Texas, Mr Trump said the envoy will "be coming most likely tomorrow to the White House to present me with a letter from Kim Jong-un".
President Trump cancelled the 12 June summit, but both sides have since made fresh efforts to revive the plan.
Scheduled to happen in Singapore, the historic meeting between Mr Trump and Kim Jong-un would be the first between sitting US and North Korean leaders.
What do we know of the first meeting?
Thursday's talks concluded early due to progress being made, a US state department official said.
Mr Pompeo tweeted after the meeting that the talks had been "substantive".
On Wednesday evening, Mr Pompeo and Gen Kim arrived separately at a building close to the UN headquarters.
Emerging later, Mr Pompeo tweeted: "Good working dinner with Kim Yong Chol in New York tonight. Steak, corn, and cheese on the menu."
North Korea has strongly objected to statements by Trump administration members comparing North Korean denuclearisation to Libya's.
Former Libyan leader Colonel Gaddafi gave up his nuclear programme only for him to be killed by Western-backed rebels a few years later.
White House spokeswoman Sarah Sanders confirmed the US and North Korean leaders still planned to meet next month.
"As the president says, if it happens, we'll certainly be ready," she said.