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The inter-Korean summit will be a litmus test for another meeting Kim has recently proposed to US President Donald Trump, giving clues to whether Kim is serious about denuclearisation, a commitment he made at their first encounter in June.
Trump has asked Moon to be "chief negotiator" between himself and Kim, according to Moon's aides, after Trump cancelled a trip to Pyongyang by his secretary of state last month.
Washington wants to see concrete signs of denuclearisation by North Korea before agreeing to a key goal of Pyongyang - declaring an end to the 1950-53 Korean War.
"I'd like to have frank dialogue with Chairman Kim on how to find a point of contact between US demands for denuclearisation and North Korea's demands for ending hostile relations and security guarantees," Moon told a meeting with senior secretaries on Monday.
Underscoring the challenges ahead, North Korea's official Rodong Sinmun said on Tuesday "the responsibility falls squarely on the United States" for the stalled nuclear discussions.
"It is due to its nonsensical, irrational stubbornness that other issues can only be discussed after our country has completely verifiably, irreversibly dismantled our nuclear capabilities... without showing the intention to build trust including declaring the end of war," the newspaper said in an editorial.
Moon, himself the offspring of a family displaced by the war, flew to the North's capital of Pyongyang, with landing expected at 10am. He will be greeted by Kim before an official welcoming ceremony, his chief of staff Im Jong-seok told a news briefing on Monday.
The two leaders will sit down for formal talks after lunch, which will be followed by a musical performance and welcome dinner.
Accompanying corporate executives, including Samsung Electronics Vice Chairman Jay Y. Lee and the chiefs of SK Group and LG Group, will meet with North Korean Deputy Prime Minister Ri Ryong Nam in charge of economic affairs, Im said.
On Wednesday, Moon and Kim are expected to unveil a joint statement, and a separate military pact designed to defuse tensions and prevent armed clashes, Im said.
Moon will return home early Thursday.
This week's summit comes as the United States presses other countries to strictly observe UN sanctions aimed at choking off funding for Pyongyang's nuclear and ballistic missile programmes, amid growing evidence that North Korea is continuing nuclear weapons development. US Ambassador to the United Nations Nikki Haley accused Russia on Monday of "cheating" on UN sanctions on North Korea.
Moon is hoping to engineer a proposal that combines a concrete framework for the North's denuclearisation and a joint declaration ending the Korean War, Seoul officials said.
The war ended with an armistice, not a peace treaty, leaving US-led UN forces including South Korea technically still at war with the North.
But US officials remain "unenthusiastic" about declaring an end to the war without any substantial action toward denuclearisation from the North, Seoul officials said.
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.
Agreeing on a timetable is a core task for Moon, as it would induce US action, said Lee Jung-chul, a professor at Soongsil University in Seoul.
"Given US scepticism that South Korea may have oversold Kim's willingness to denuclearise, how President Moon delivers his sincerity toward denuclearisation to Trump would be a key factor for the fate of their second summit," Lee told a forum on Monday in Seoul.