"My message in Japan, my message in South Korea, my message in meeting with leaders of both of those countries is that we are going to continue to stand together along with our other allies and partners to continue to intensify the economic and diplomatic pressure on North Korea until they permanently abandon their nuclear and ballistic-missile program", Pence said.
Though Moon has used the Olympics to resurrect meaningful communication with North Korea after a diplomatic stalemate over its nuclear program, he didn't immediately jump on the North Korean offer for a summit.
The United States and South Korea have agreed on terms for further diplomatic engagement with North Korea, first with Seoul and then possibly leading to direct talks with Washington without pre-conditions, Vice President Mike Pence said in a newspaper interview published on Sunday. Mr. Moon has said in the past that he only wanted to meet the North Korean leader if they can make progress on nuclear issues.
And Kim's sister, Kim Yo-jong, made history by becoming the first member of the North's ruling family to visit the South since the Korean War in the mid-20th century.
Invited by Moon for lunch at Seoul's presidential palace, Kim Yo Jong verbally delivered her brother's hope for a summit with Moon in Pyongyang, a meeting that she said would help significantly improve ties after an extended period of animosity. South Korea's presidential Blue House also had no immediate comment.
Last year, North Korea conducted dozens of missile launches and its sixth and largest nuclear test in defiance of U.N. Security Council resolutions as it pursues its goal of developing a nuclear-armed missile capable of reaching the United States.
South Korea may also need to persuade traditional allies the United States and Japan, which have raised concerns that the North is attempting to use its outreach as a release valve for worldwide pressure. The White House official said the invitation didn't undermine or detract from Pence's trip.
"The vice president is grateful that President Moon reaffirmed his strong commitment to the global maximum pressure campaign and for his support for continued sanctions", Pence spokeswoman Alyssa Farah said when asked about the developments.
Days later, TV news shows in South Korea are still repeatedly airing footage of Kim walking with President Moon Jae-in, often with a placid smile on her face.
Moon has expressed hope the détente could lead to a broader dialogue with the United States. But the two sides rebuffed his efforts to organize a meeting between them during the games. The two did not interact - although Pence, who arrived late, greeted the other dignitaries around him - prompting criticism of the American vice president.
"You must have had a hard time due to the cold weather", Moon said as he greeted Kim Yo-jong, referring to the frigid temperatures during Friday's opening ceremony.
In its efforts to bring North Korea to the Pyeongchang Games, South Korea paused joint military exercises with the US and relaxed a series of sanctions, including on individuals like Ms. Kim.