In an unprecedented visit to the White House for a top North Korean official, former spy chief Kim Yong Chol will hand a letter from his leader Kim Jong Un to United States President Donald Trump as the two sides inch towards a summit.
On Thursday, Mr Trump, on board his plane while heading to Texas, told Reuters that he was still hoping for a summit with Mr Kim Jong Un on June 12 in Singapore.
But he emphasised that it may take more than one meeting to reach an agreement.
"There is a very good chance that it won't be done in one meeting or two meetings or three meetings. But it will get done at some point. It may get done really nicely and really intelligently, or it may not get done intelligently. It may have to be the hard way," he said.
"But I think it will get done in a very smart, organised fashion, and I think that Kim Jong Un wants to see it also. And I am going to be very happy when the day arrives when we can take sanctions off and have a very good relationship with the entire Korean peninsula."
Mr Trump said that he would like to see "a total denuclearisation in as quick a period of time as is practicable".
"You are talking about machinery, you are talking about things that can't necessarily happen immediately, but they can happen in as rapid a fashion as they can happen. That is what I want to happen."
In Pyongyang, Mr Kim Jong Un reaffirmed, during a meeting with Russian Foreign Minister Sergei Lavrov on Thursday that he was committed to the denuclearisation of the Korean peninsula, and expressed hope for a phased process in resolving the issue, the state-owned Korean Central News Agency (KCNA) reported.
"The DPRK's will for denuclearisation of the Korean peninsula still remains unchanged and consistent and fixed," the KCNA quoted Mr Kim Jong Un as saying in English.
"And he hoped that the DPRK-US relations and the denuclearisation of the Korean peninsula will be solved on a stage-by-stage basis."
DPRK, or Democratic People's Republic of Korea, is North Korea's formal name.
Speaking to journalists in New York after his meetings with General Kim Yong Chol, US Secretary of State Mike Pompeo said: "We have made real progress in the last 72 hours towards setting the conditions. 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.
"I have had the chance to meet Chairman Kim Jong Un twice and now Kim Yong Chol three times... I believe they are contemplating a path forward where they can make a strategic shift, one that their country has not been prepared to make before."
But he also cautioned: "They will have to choose a path that is fundamentally different than the one that their country has proceeded on for decades. It should not be to anyone's surprise that there will be moments along the way that this won't be straightforward."
Referring to the challenges ahead, he said: "We are decades into this challenge, and so one not ought to be either surprised or frightened or deterred by moments where it looks like there are challenges and difficulties, things that can't be bridged. Our mission is to bridge them so that we can achieve this historic outcome."
Mr Pompeo stressed that there was "no daylight" between the US and its allies, Japan and South Korea. Japan is concerned about being in the range of North Korean missiles and wants to resolve the emotional issue of Japanese citizens abducted by North Korea.
"We understand their concerns," Mr Pompeo said. "We understand the risks that can be posed to them. And an agreement that we reach will provide an outcome that each of those countries can sign on to as well."
On his plane, Mr Trump said a deal with North Korea would also cover its missile programme.
"It means missiles," he said.