Moon expressed his gratitude to Trump for sending a high-ranking USA delegation, including Vice President Mike Pence, to the South Korea-hosted Winter Olympics.
Talking to the media at the airport, Won said, "I send regards from our people of the North to the people in the South".
The official Korean Central News Agency (KCNA) said in a commentary late yesterday that US Vice-President Mike Pence claimed that he would go to the Winter Olympics to hold back the North Korea's "propaganda offensive". The International Olympic Committee later allowed them and 20 other athletes to compete in the February 9-25 games in special entries given to the North as it worked out a set of Olympics-related rapprochement deals with South Korea.
The development between the two countries has brought some ease into their strained relations.
He met North Korean defector Ji Seong-ho whose flight to freedom was highlighted in Mr Trump's State of the Union address this week.
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The HTC engineers will remain in Taipei, turning Taiwan into Google's most significant engineering hub in the Asia-Pacific region. The HTC deal marks Google's latest foray into the smartphone market, with its focus now on its Pixel high-end Android handsets .
While it has repeatedly said it prefers a diplomatic solution, Trump has exchanged threats with Kim and US officials have said the president and his advisers have discussed a preventative "bloody nose" strike on North Korea, alarming experts who warn that this could trigger catastrophic retaliation, especially on South Korea.
Joseph Yun, the USA special envoy on North Korea, said on Thursday he did not think the administration was close to triggering military action.
And he praised Mr Trump for "sending out a warning" when he spoke of human rights violations in North Korea. It probably will come as a big threat to the North Korean regime.
"Nobody has the right to take issue" with the event, said Rodong Sinmun, the official daily of North Korea's ruling Workers' Party.