Moon was all smiles Saturday as he greeted Kim Yo Jong, the sister of North Korean dictator Kim Jong Un, and Kim Yong Nam, the country's 90-year-old nominal head of state, for lunch at the presidential residence.
While Kim Jong Un expressed his willingness to improve inter-Korean ties in a personal letter delivered by his younger sister Yo Jong to Moon, the South Korean president stressed the involvement of the United States, saying, "U.S".
It would be the first summit in more than a decade between Korean leaders.
The daughter of the country's late leader Kim Jong Il also acted as an aide to her father in his later years. That sends an implicit message that North Korea can maintain its nuclear weapons and still be welcomed by the worldwide community to participate in this important global event.
South Korean President Moon Jae-in met with the delegation Saturday at the presidential Blue House in Seoul.
"In the midst of all of this, he (North Korean leader Kim Jong Un) ran a military parade that highlighted his ballistic missiles", Mattis told reporters on his plane en route to Rome on the first leg of a European tour.
The North's representative, its highest-level official ever to visit the South, was placed between Olympics chief Thomas Bach and United Nations secretary-general Antonio Guterres.
Korean ski coach says it's 'honor' to compete in Olympics
Analysts believe its diplomacy is seeking to weaken the measures against it, and could be trying to loosen the alliance between Seoul and Washington.
Speaking on his way home from the Winter Olympics in South Korea, Mr Pence said there was "no daylight" between the two allies on the issue. US Vice-President Mike Pence, sitting a few seats away in the same Opening Ceremony VIP booth, looked stony faced as the scene unfolded.
He also reiterated the Trump administration's stance that the U.S. would take whatever "action is necessary to defend our homeland", including military operations, as it seeks to denuclearise the North.
At the opening ceremony of the Olympics on Friday night, Moon and Kim Yo Jong shook hands in what appeared to be a friendly manner.
While a summit in Pyongyang would signal warming ties on the peninsula, it also risks driving a wedge in the alliance between the USA and South Korea.
"What's the point of having an inter-Korean summit if it separates the US and South Korea, and North Korea gets off the hook?" They technically remain at war, and no member of the Kim family has set foot in South Korea since the end of hostilities in the Korean War in 1953.
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