While both Trump and Kim have appeared eager to hold the summit, the two sides have remained far apart on the key issue of denuclearization, with North Korea rejecting US demands for it to unilaterally abandon a nuclear weapons program that now threatens the United States.
Significant differences, however, remain - especially over the USA and North Korean definition of "complete denuclearization".
The summit was originally scheduled for June 12 in Singapore.
Now his travel restrictions seem to have been further relaxed amid efforts to organise the Kim-Trump Summit in Singapore.
"We're talking to them now", he said Friday. His many positions in party and government make him one of the most powerful people in North Korea, according to the website North Korea Leadership Watch.
The US and North Korea are seeking common ground on the steps it would take for Kim Jong-un to give up his nuclear weapons.
Kim Chang-son, a close aide of North Korea's ruling Kim family and high-level party official, had also been spotted in Beijing on Saturday.
Howard X also made an appearance as Kim at the Winter Olympics in Gangneung in South Korea in February, bewildering North Korean cheerleaders who initially thought their leader had walked into a hockey stadium.
The two teams met yesterday on the northern side of Panmunjom.
It's unclear who Kim will be meeting with while in the USA, though he is the highest-level North Korean official to step foot in the country since 2000.
The three-way summit, if held, will likely be aimed at providing a security guarantee for North Korea in exchange for its denuclearization.
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South Korean media also reported that a North Korean delegation arrived in Singapore on Monday night, where other USA officials, led by White House deputy chief of staff Joe Hagin, are preparing for the summit.
Moon has played a critical role in delivering the positions of each side to the other while encouraging them to speak to each other, Yoon said.
South Korean President Moon Jae-in could make a trip to Singapore for a three-way summit with his US and North Korean counterparts next month, depending on the outcome of ongoing discussions between Washington and Pyongyang, a ranking government official here said Monday.
Kim Yong Chol, who is about 72, is a contentious figure outside North Korea.
But Kim, through two summits with Chinese President Xi Jinping in March and May, has called for a phased and synchronised process in which every action he takes is met with a reciprocal reward from the United States.
But following Pyongyang's conciliatory gesture and Seoul's mediation, Trump suggested that the summit could go ahead as planned.
"It looked like the real Kim Jong Un, but later I realised it's not the real one", said Sagar Admuthe who was visiting from Mumbai, India, after several selfies with the doppleganger against a backdrop of the city's bay.
US and South Korean officials haven't confirmed the details of the pre-summit negotiations between Washington and Pyongyang at the border.
He "will be authorized to speak on behalf of Kim Jong Un, and his intricate knowledge of the various policy issues at play means that US officials will regard what he says as a bellwether for the DPRK's intentions at the summit".
The North Koreans, after expressing initial enthusiasm about diplomacy with the United States earlier this month, did not show up for a preparatory meeting in Singapore, threatened to use nuclear force, and referred to U.S. Vice President Mike Pence as a "political dummy".
The U.S. has called for "complete, verifiable and irreversible" dismantling of Pyongyang's nuclear arsenal.