Kim Jong Un invites South Korean President Moon Jae-in to a summit in the North

A spokesman for the Moon said he did not immediately accept the invite.

The spokesman said Moon did not immediately agree to a meeting, adding that the two countries should continue to work on creating a political atmosphere that would make such a meeting feasible.

Moon also told Kim's sister that the North should have a dialogue with the U.S.

Following the meeting, Pence press secretary Alyssa Farah said in a statement, "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."

The luncheon also included Choe Hwi, chairman of the North's National Sports Guidance Committee, and Ri Son Gwon, chairman of the agency that deals with inter-Korean affairs.

The meeting took place after Kim Yo Jong and other North Korean delegates attended the Olympics' opening ceremony. She was photographed sitting behind Vice President Mike Pence during the ceremony.