"I am happy to meet you," Moon told Kim before the visitor stepped over the line, making him the first North Korean leader to set foot in the South since the Korean War ended in an armistice 65 years ago.
The two men briefly stepped back over the line into the North before walking to the Peace House building on the southern side of the truce village of Panmunjom for the summit -- only the third of its kind since hostilities ceased in 1953.
It is the highest-level encounter yet in a whirlwind of nuclear diplomacy, and intended to pave the way for a much-anticipated encounter between Kim and US President Donald Trump.
In the most detailed direct reference to the process by Pyongyang so far, the North's official KCNA news agency said Friday that Kim will "open-heartedly discuss... all the issues arising in improving inter-Korean relations and achieving peace, prosperity and reunification of the Korean peninsula".
It did not mention denuclearisation, but the North's atomic arsenal will be high on the agenda at the talks.
Last year Pyongyang carried out its sixth nuclear blast, by far its most powerful to date, and launched missiles capable of reaching the US mainland.
Its actions sent tensions soaring as Kim and Trump traded personal insults and threats of war.
Moon seized on the South's Winter Olympics as an opportunity to broker dialogue between them, and has said his meeting with Kim will serve to set up the summit between Pyongyang and Washington.
Trump has demanded the North give up its weapons, and Washington is pressing for it to do so in a complete, verifiable and irreversible way.
But Seoul played down expectations Thursday, saying the North's technological advances with its nuclear and missile programmes meant any deal would be "fundamentally different in nature from denuclearisation agreements in 1990s and early 2000s".
"That's what makes this summit all the more difficult," the chief of the South's presidential secretariat Im Jong-seok told reporters.
- Peace and denuclearisation -
Pyongyang is demanding as yet unspecified security guarantees to discuss its arsenal.
When Kim visited the North's key backer Beijing last month in only his first foreign trip as leader, China's official Xinhua news agency cited him saying that the issue could be resolved, as long as Seoul and Washington take "progressive and synchronous measures for the realisation of peace".
In the past, North Korean support for denuclearisation of the "Korean peninsula" has been code for the removal of US troops from the South and the end of its nuclear umbrella over its security ally -- prospects unthinkable in Washington.
"The big issues we know are peace and denuclearisation," Yonsei University professor John Delury told AFP.
The two Koreas "can do a lot more on peace than on denuclearisation", he said, but the post-summit statement will give "a lot of chance to analyse every word, reading between the lines, look for things that are there and not there".
Pyongyang announced last week a moratorium on nuclear tests and intercontinental ballistic missiles, adding it would dismantle its Punggye-ri nuclear test site.
But it also said it had completed the development of its weapons and had no need for further tests.
Seoul has also promoted the idea of opening talks towards a peace treaty to formally end the 1950-53 Korean War, when hostilities stopped with a ceasefire, leaving the neighbours technically in a state of conflict.
Reunions of families left divided by the war could also be discussed at the summit, and Moon has told Japanese Prime Minister Shinzo Abe he will raise the emotive subject of Japanese citizens kidnapped by the North.
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