The U.S. and North Korea agreed Sunday to hold a second summit between leaders Donald Trump and Kim Jong Un "as soon as possible," according to a statement by South Korea's presidential office, with the American side saying that Kim had also invited inspectors to a key nuclear facility. The Blue House released the statement after U.S. Secretary of State Mike Pompeo met in Seoul with South Korean President Moon Jae-in to discuss his meeting with Kim in Pyongyang earlier the same day. Later, the U.S. State Department said Pompeo and Kim had "refined options for the location and date of that next summit." On the denuclearization committed to at the leaders' first summit in Singapore, Kim told Pompeo that inspectors were invited to visit the Punggye-ri nuclear test site "to confirm that it has been irreversibly dismantled," according to a statement from spokeswoman Heather Nauert. Trump tweeted Sunday that he looked forward to meeting Kim again "in the near future." On arriving in South Korea, Pompeo indicated he had made progress in talks with the North Korean leader over the denuclearization of the Korean Peninsula.