Mr Moon and his wife, Kim Jung-sook, were greeted by Mr Kim and his wife, Ri Sol-ju.
The two leaders began official talks on Tuesday afternoon, after parading down the streets of Pyongyang in Kim's black Mercedes limousine to loud cheers from almost 100,000 North Koreans who waved flowers and chanted "Unification!" The leaders held their first two meetings on April 27 and May 26 this year at the border village of Panmunjom.
A welcoming mood prevailed in the North Korean capital, with thousands of citizens lining the streets holding pom-poms and flags as Moon and North Korean leader Kim Jong Un passed by waving from the rear of an open-backed limousine.
South Korea will be seeking to cement a breakthrough in faltering nuclear talks between Pyongyang and Washington.
But he said he still expects the summit to produce meaningful agreements that "fundamentally remove the danger of armed clashes and ease fears of war" between the two Koreas.
Moon echoed this sentiment, saying he hopes to "find an intersecting point between the United States' call for denuclearization steps and the North's demand for corresponding steps to guarantee its security and end the hostile relationship (between the US and North Korea)". Moon can not lean too far forward on inter-Korean reconciliation without repeating past mistakes and playing into Pyongyang's hands by weakening the U.S.
But there are still concerns in Washington that Moon may push his agenda too fast at the cost of hampering the alliance.
The South's president is also scheduled to attend a concert and visit key sites in the North's capital with his delegation, which includes tycoons Lee Jae-yong - the heir to the Samsung group - and the vice chairman of Hyundai Motor.
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South Korea is pinning high hopes on Kim's remarks to Moon's special envoys earlier this month that he wants to achieve denuclearisation within Trump's first term in office ending in early 2021, the first time line he has given. We did see some live feeds today after President Moon's departure from Seoul Air Base.
"Depending on how candidly the two leaders talk through the issue, whether any concrete agreement on denuclearization can be reached, and if that can make it to a joint statement, if not a statement, whether a verbal agreement can be reached and be announced, all these questions are blank ones for us at the moment", he said.
People watch a TV screen showing South Korean President Moon Jae-in being welcomed by North Korean leader Kim Jong Un upon his arrival at the airport in Pyongyang, North Korea, on September 18, 2018.
Still, Im said Seoul will "push to resume genuine dialogue for the establishment of a new peaceful relationship ... so that the progressive denuclearization of North Korea and reciprocal US actions can be pursued". Moon is hoping to mediate an impasse between the United states and the North over the latter's nuclear weapons programme.
The inter-Korean summit will be a litmus test for another meeting Kim has recently proposed to U.S. President Donald Trump, giving clues to whether Kim is serious about denuclearisation, a commitment he made at their first encounter in June.
He has been pushing inter-Korean economic cooperation but several South Korean newspapers urged caution Monday, with the Korea Herald calling the businessmen's presence on the trip "untimely".
North Korea maintains that it has developed its nuclear weapons to the point that it can now defend itself against a potential US attack, and can now shift its focus to economic development and improved ties with the South. The entire ceremony lasted about 15 minutes before Moon and Kim drove off in a caravan of black cars and the crowd quickly returned to its previously calm state. Those trips produced a slew of inter-Korean rapprochement projects, which were suspended after conservatives took power in Seoul.