South Korean National Security Office Head Chung Eui-yong revealed few details of the trip as he boarded a plane at Seoul's Incheon Airport for a brief two-day visit to Washington.
A senior USA administration official said no decision on the possibility of the United States joining a summit of North and South Korea was expected to be made at this week's meeting with McMaster.
Moon still described the outcome of his envoys' North Korea trip "a big step toward denuclearization of the Korean Peninsula" that was possible with "a strong support" by the US government.
Other U.S. officials voiced greater skepticism Tuesday, reflecting the mammoth questions about North Korea's intentions.
Under Kim Jong-un, North Korea has accelerated its programme of missile testing and nuclear weapons development at an unprecedented pace, while under Donald Trump, the United States has responded with threats of "fire and fury like the world has never seen".
Talks began on Wednesday on cost-sharing for the United States military presence on the Korean peninsula.
The Seoul officials said North Korea offered talks with the United States over normalizing ties and denuclearization of the Korean Peninsula.
While in the past it was possible to test the North Koreans and let the process play out, the official said, the USA and its allies are now running out of time as North Korea inches closer to mastering a deliverable nuclear weapon. On multiple occasions, official statements from the ruling party of North Korea have bore a stronger resemblance to professional wrestling than formal diplomacy, threatening dramatic and destructive displays of Kim's nuclear might and calling the nation's nuclear future "non negotiable".
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In its Wednesday tirade, Rodong Sinmun insisted that the real nuclear threat facing the planet is the United States.
Little is known about the delegations' visit to the United States, including who they'll be meeting with and what they'll be telling their allies about the North Korea meeting.
Coming after the North's participation in the Pyeongchang Winter Olympics last month, the meeting in Pyongyang represents continuing momentum for dialogue.
"She is the most powerful weapon of North Korea now", the source told the Post. The two Koreas also agreed to hold a summit between Kim and South Korean President Moon Jae-in in late April.
"That's far from the complete, verifiable, irreversible denuclearisation that the U.S. expects", Koh added. The Trump administration also pushed through some of the harshest economic sanctions any country has ever faced.
The State Department's roster of senior diplomats dealing with and experienced on North Korea is seriously depleted. They further reported that the North was open to negotiations with the USA and could suspend all missile and nuclear tests during this period.
"Kim Jong-un has a certain message, which is not publicized to be delivered directly to the Trump administration", the source told the Post, speaking on condition of anonymity.
The article does not mention the possibility of denuclearization, though it does appear to serve more towards explaining how North Korea chose to pursue its illegal nuclear weapons program rather than insisting that Pyongyang will keep the weapons.
Mr Kim's agreement to denuclearisation talks is no guarantee that North Korea will start dismantling its arsenal.
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