Kim Yo Jong is in South Korea for the Winter Olympics, hosted in Pyeongchang and featuring united Korean teams.
Moon urged Pyongyang to actively seek an "absolutely necessary" dialogue with Washington, he said.
This would be the first meeting between Korean leaders in more than a decade, and it marks a significant, if at present mostly symbolic, step toward rapprochement on the divided peninsula. The daily said the two sides "discussed a range of issues concerning the two Koreas".
U.S. President Donald Trump and the North Korean leadership traded insults and threats of nuclear war as tensions rose, with Trump repeatedly dismissing the prospect or value of talks with North Korea.
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A source also told TMZ , "They are worth more as a group than they are individually, so this is a great venture for all of them". She added, "There's something so strong in the message of what the Spice Girls stood for". " It was so great to see the girls ".
He also met Kim Jong-un's sister, Kim Yo-jong, at the opening ceremony of the Olympic Games in PyeongChang later on the same day.
"There is no daylight between the United States, the Republic of Korea and Japan on the need to continue to isolate North Korea economically and diplomatically until they abandon their nuclear and ballistic missile program", Pence told reporters on his flight back to the United States.
As they shook hands, the North and South Koreans spoke briefly.
U.S. Vice President Mike Pence and his wife arrived after the handshakes.
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Medicare: Repeal the Independent Payment Advisory Board (IPAB), a Medicare cost-cutting group created by the Affordable Care Act. That was a turnaround from Tuesday, when Mr Trump had said he would "love" a shutdown if he did not get his way on immigration .
The two Koreas technically remain at war, as the Korean War ended with an armistice, not a peace treaty.
North Korea's decision to participate has eased tensions after months of saber rattling and missile and nuclear tests that have raised fears it's closer-than-expected to achieving its goal of developing a nuclear weapon that could reach the USA mainland.
Pence and the North Korean delegation, who both attended the Games opening ceremony, had no contact with each other.
North Korean leader Kim Jung Un reportedly selected the looks himself, not all that surprising considering the authoritarian ruler's penchant for - or evolution toward - a snazzy suit and "trend-setting" haircuts.
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He said: "He's my friend before being another player or team-mate, so what we say is personal, not about football". Agree they all 3 need to start & kenedy & slimani are better than what we have but the GK who knows?
"North Korea is not a victim - they are terrorists", Warmbier said in September.