The meeting will serve as a prelude for the summit that US President Donald Trump is planning with Kim in late May or early June, in a location still being decided.
Trump has confirmed reports that Mike Pompeo, the head of the CIA and nominee to be secretary of state, visited Pyongyang recently and met Kim as part of the preparations. This is the highest-level meeting between the United States and North Korea since then-Secretary of State Madeleine Albright went to Pyongyang in 2000 to meet Kim's father.
"Mike Pompeo met with Kim Jong Un in North Korea last week," Trump tweeted today. "Meeting went very smoothly and a good relationship was formed. Details of Summit are being worked out now. Denuclearisation will be a great thing for World, but also for North Korea!"
Trump, who prides himself on being a master negotiator but also has a penchant for the limelight, is playing up the prospect of persuading Kim to relinquish his nuclear weapons programme.
That is a goal that has eluded US negotiators for more than two decades, and many analysts are sceptical that the young North Korean leader, having poured so much money and effort into the programme, will easily give it up.
But the South Korean Government is promoting the upcoming summits as an opportunity to try.
"We've been making consistent efforts to peacefully improve the inter-Korean relationship, especially dealing with the North Korean nuclear issue and denuclearisation of the peninsula, with the goal of peace on the Korean Peninsula," said Chung Eui Yong, the South Korean national security adviser who has met Kim and Trump to arrange the summits.
Chung said that South Korea would work to guarantee North Korea's security and the regime's "bright future" while persuading it to give up its nuclear weapons.
He reiterated South Korea's "gratitude" for Trump's efforts to make progress on the issue, even as he warned against "blind optimism," given the magnitude of the problem.
The two Koreas have been in a technical state of war for the past six decades because the Korean War ended in an armistice, not a peace treaty, in 1953.
The armistice agreement, which was brokered in the same place in the demilitarised zone where Kim and Moon will meet next week, was signed by the US on behalf of the United Nations, and by North Korea and China on the other side.
The Kim dynasty has kept the country on a war footing and anti-American sentiment alive all this time as part of its propaganda justifying the family's ongoing rule. It has also said North Korea needs nuclear weapons to defend itself against a "hostile" United States.
During the last inter-Korean summit in 2007, the two sides discussed ending the armistice but did not make any progress toward a peace treaty.
Any peace treaty must necessarily involve the United States, and it may come with a North Korean insistence that American troops are no longer needed in the southern half of the peninsula.
"Pyongyang has signalled to Washington its willingness to work towards denuclearisation, although it may still disagree with Washington on the specific steps to achieve that goal," said Koh Yu Hwan, a professor of North Korean studies at Dongkuk University in Seoul and one of the experts advising negotiators.
Withdrawing US forces from the Korean Peninsula was one of the five requirements for denuclearisation that North Korea proposed in a 2016 statement.
"At this point, however, Kim Jong Un seems not to be pushing for this as an immediate condition for talks," Koh said.
For South Korea, much is riding on the summits.
There was widespread fear here at the end of last year that Trump was serious about conducting military strikes on North Korea to take out its nuclear weapons programme, an action that would put Seoul at risk of attack by North Korea. The entire capital region, home to 25 million people, is within range of North Korea's conventional artillery.
But Moon, a progressive who has sought engagement with the North, has assiduously worked to promote diplomacy.
He used the Winter Olympics, which South Korea hosted in February, to invite senior North Koreans, including the leader's influential sister, to the South. And he has not hesitated to heap praise on Trump and credit him with North Korea's change of heart.
The Blue House is busy laying the groundwork for the meeting. It has set up a summit preparation committee, led by Moon's chief of staff, Im Jong Seok, who was closely involved in the previous two inter-Korean summits.
It has also formed two advisory committees comprising about 50 experts on North Korea. They have been giving the summit organisers regular advice in their areas of expertise, according to several committee members.
A hotline between the two leaders - a first - is expected to be connected tomorrow. Their first call is expected before Moon and Kim meet face to face in "Peace House," a large, four-storey building just on the southern side of the line that has divided the two Koreas for more than six decades. By crossing it, Kim will become the first North Korean leader to come to the South since the Korean War.
Moon's two progressive predecessors both held summits with the North Korean leader at the time, Kim Jong Un's father, but both went to Pyongyang to meet him.
As part of summit preparations, South Korea is renovating the "Peace House" at Panmunjom village in the demilitarised zone, remodelling a second-floor room where Moon and Kim will meet and a third-floor room that can be used as a banquet hall, according to local reports.
One newspaper, the Kukmin Ilbo, reported that the construction included the installation of bulletproof glass and technology to prevent the rooms from being bugged.
There is also speculation that a banquet will be held after the meeting and that the first ladies may join.
The village, about 55km north of Seoul, has become emblematic of the standoff, with soldiers from both Koreas - men with the same language and culture - physically facing off on a daily basis.
Kim's wife, Ri Sol Ju, has been taking on an increasingly high profile in recent weeks, meeting the South Korean envoys for dinner in Pyongyang, travelling with Kim to a summit in Beijing, and hosting a Chinese delegation at the weekend.
Coincidentally, Moon's wife, Kim Jung Sook, has the same name as Kim Jong Un's grandmother, who is celebrated in North Korea's personality cult as a revolutionary martyr and the mother of the nation.
