One of Kim Jong-un's most senior officials is thought to be travelling to the United States, as preparations for a possible historic summit gather pace.
President Donald Trump halted new sanctions aimed at putting pressure on Kim Jong Un.
Nauert provided no further details.
Since then, North Korea has rejected US demands for it to unilaterally abandon its nuclear weapons programme that experts say could threaten the United States.
"It will happen!" Trump said, confirming that a U.S. team "has arrived in North Korea to make arrangements for the summit" between himself and North Korean leader.
Mr Trump said on Saturday (local time) he was still looking at a June 12 date for a summit in Singapore and that talks were progressing very well.
Mr. Moon said Mr. Kim wanted to discuss "complete denuclearization of the Korean Peninsula" with Mr. Trump.
Yonhap said Kim Yong Chol's name was on the passenger list for a flight Wednesday from Beijing to NY.
Relations between the two Koreas had chilled in recent weeks, with North Korea canceling a high-level meeting with Seoul over South Korea's participation in regular military exercises with the United States and insisting that it will not return to talks unless its grievances are resolved.
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Hooker was also a part of a USA delegation led by Ivanka Trump, daughter of the president and his senior adviser, that attended the closing ceremony of the PyeongChang Winter Olympics at the end of February.
With the landmark US-North Korea summit moving along "very nicely" according to US President Donald Trump, Singaporeans were surprised to see Kim Jong Un gamely posing for pictures in the heart of Marina Bay yesterday, armed with a durian and a box of chicken rice.
"This combination of positions in the party and state makes Kim one of the most powerful figures in North Korea", according to North Korea Leadership Watch, a website that tracks senior regime figures".
Another "pre-advance" team is heading to Singapore to meet with North Koreans, the White House said.
South Korea is reviewing ways to address North Korea's security concerns, including converting the current armistice into a peace agreement, a senior Moon administration official said on Sunday.
Criticising the United States leader directly, Lord Hague added: "Trump is the one American leader of recent decades who could agree to that".
The general has always been a right hand man to North Korea's leader, playing a front-seat role during recent rounds of diplomacy aimed at ending the nuclear stalemate on the Korean peninsula. But experts are hardly optimistic about a breakthrough, even if the meeting goes ahead.
The State Department said earlier that a team was in Panmunjom, which straddles the border inside the demilitarized zone, or DMZ, separating the North and South Korea.
North Korea has rejected the US's demand for it to unilaterally abandon its nuclear weapons programme. "He didn't give in to frustration, he gave Kim a platform to say some things about denuclearization that will play well in the USA, and he again showed Trump the mesmerizing all-consuming media impact that a summit can have - something that's bound to appeal".
The United States and the United Nations over the last several years have been able to ban most of North Korea's trade and cut off a large portion its foreign income stream - including getting China to reduce trade. "It will happen!" Trump said in the same tweet.
While admitting this option remained unlikely, Lord Hague stated Kim could agree to this plan if a formal treaty were ratified in the US Senate to provide a "security guarantee". "But he wants to give off this perception that he's this open leader, that he's peaceful, that he's reasonable".
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