Kim invited Moon to step briefly across the demarcation line into North Korea, before the two leaders crossed back into South Korea holding hands.
A historic moment for both Koreas.
It would be the first meeting of North and South Korean leaders in more than 10 years.
Kim Yo Jong would be the first member of the Kim family to cross the border to the South.
UN Command says North Koreans violated border rules during the chase.
"The world cannot tolerate the menace of a rogue regime that threatens it with nuclear devastation."
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