Moon hosted talks and a lunch with Kim Yo Jong, the younger sister of the North Korean leader, at the presidential Blue House in Seoul.
On Saturday, she sat down for almost three hours of meetings and lunch at the Blue House, South Korea's presidential complex.
Kim's sister Kim Yo Jong, who is visiting South Korea to attend the Pyeongchang Winter Olympics, delivered her brother's personal invitation during a meeting with Moon at the Blue House, a presidential spokesman said.
In South Korea and beyond, commentators are taken with Kim's surprisingly stylish and relaxed demeanor.
During Mr. Pences visit, Mr. Moon assured the Vice President he would tell the North Koreans clearly that they would not get economic or diplomatic concessions for just talking, only for taking concrete steps toward denuclearization, the newspaper said.
Observers believe the two countries will seek to conduct the leaders' meeting in short order.
Rome: US Defence Secretary Jim Mattis cast doubt Sunday on whether North Korea's charm offensive at the Winter Olympics would lead to a lasting rapprochement between Pyongyang and Seoul.
President Donald Trump's administration has taken a hard line on North Korea's nuclear and ballistic missile programme, saying there is no room for negotiations unless Pyongyang abandons it. "But this is a good beginning", Mr. Breen said - one that raises the possibility of more talks between the worldwide community and the world's most isolated regime.
The North Korean delegation arrived in the South on Kim's private plane on Friday via Incheon worldwide airport to attend the opening ceremony of the Pyongchang Winter Olympics where Seoul and Pyongyang are represented by joint teams.
But the invitation to Pyongyang thrusts Mr. Moon into a potentially delicate diplomatic dance, as South Korea's allies and neighbours maintain a hardline stance toward Mr. Kim and his weapons program.
Not everybody was so taken by the show of Korean unity, with U.S. Vice President Mike Pence remaining seated as the North and South Koreans entered the stadium. There's even speculation of a summit between Kim and Moon.
It gives him "the rationale or the excuse to work on some moderation of the sanctions and possibly the scale and timing of the military exercises", said former South Korean Foreign Minister Han Seung-joo, in an interview.
She's not what we expected: not stiff, but smiling.
"If there is a message to be conveyed to South Korea or the US, she is amply well positioned to convey it", he said.
Mr. Trump, who has at times exchanged taunts and threats with Mr. Kim, said in early January after the first intra-Korean talks in over two years that the United States was willing to speak to North Korea "under the right circumstances", although it was far from clear whether this would pay dividends.
"They wanted to send a message of being not aggressive, of being somewhat more friendly and pliable", he said.
Still, it wouldn't be South Korea if people weren't asking the perennial question when it comes to North Korea changing gears and showering its rival with apparent affection: What's in it for Pyongyang?
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