Moon was expected to have talks with Kim on Tuesday and Wednesday, according to Moon's chief of staff. Moon and Kim were also expected to hold a joint news conference on Wednesday if their two sets of summit meetings go smoothly.
Prior to his departure, the South Korean leader said he would push Kim for "irreversible, permanent peace" and better communication between Pyongyang and Washington. -North Korean relations back on track, Moon might try to, among other things, seek more reassurance from North Korea that an end-of-war declaration would not mean the withdrawal of USA troops from South Korea, Aum said. The North often holds off reporting stories until it has had time to review and edit the video for maximum propaganda impact.
There is yet no report on the results of the talks, which started around 3:30 p.m. local time (0630 GMT). North Korean soldiers and naval troops quick-marched into position to welcome Moon, and Kim Jong Un's sister was seen walking amid the preparations.
The North's Korean Central News Agency (KCNA) said the summit "will offer an important opportunity in further accelerating the development of inter-Korean relations that is making a new history". He added that the degree to which the matter will be discussed and the level of consensus that Moon and Kim might reach would depend on their talks.
Moon's previous meetings with Kim were at the border village of Panmunjom.
One of Moon's objectives - and one that also interests Kim - was clear from the people he took with him.
Moon is to take 16 business figures to Pyongyang, including Samsung's de facto leader, Lee Jae-yong. Currently, all major joint projects between the Koreas are stalled because of USA -led sanctions.
But the nuclear issue was sure to cast a shadow over negotiations on joint projects.
But no details were agreed and Washington and Pyongyang have since sparred over what that means and how it will be achieved.
The two leaders arrived at the Baekhwawon guesthouse, had separate luncheons, and then began the first of a three-day summit talk.
"Until recently, denuclearization was (a North-US issue), and neither the North nor the US were very happy about us raising the denuclearization issue", Im said.
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Moon said he wants "to find a middle ground between a US request for (North Korea's) denuclearization and the North's request for corresponding measures such as ending hostile relations and security assurances".
And again at Pyongyang airport she briefly joined them on a platform where they were to watch a welcome ceremony, before drifting into the cameras' vision several times as the two leaders and their wives made their way past well-wishers.
According to Cheong Wa Dae, in a recent phone conversation Trump requested that Moon act as the "chief negotiator" between the United States and North Korea.
Rarely do the North Korean official media even mention the word denuclearization.
US intelligence agencies say Kim's nuclear weapons program is continuing unabated.
Trump, ahead of that June summit, acknowledged that he talked with a visiting North Korean envoy about ending the war.
Handong Global University Professor Kim Joon-hyung called the third inter-Korean summit an extension of the first, during a Monday panel discussion in Seoul.
"It's got to be the longest war - nearly 70 years, right?" China, signaling its support for Kim's recent diplomatic moves, sent its third-highest party official to those festivities. Depending on the outcome of the talks, an inter-Korean summit agreement will be announced in the afternoon.
Some progress along those lines is already underway. But they were later suspended after conservatives took power in Seoul with hardline policies toward the North. Kim Jong Un took office in late 2011 upon the death of his father.
But war remains. That's because the Korean War ended with a military cease-fire, in the form of an armistice, not a formal peace treaty.