Donald Trump's White House on Thursday voiced hope that a Korean summit would "achieve progress toward a future of peace," as the leaders of the two countries sat down to talk.
"We are hopeful that talks will achieve progress toward a future of peace and prosperity for the entire Korean Peninsula," the White House said in a statement.
"The United States appreciates the close coordination with our ally, the Republic of Korea, and looks forward to continuing robust discussions in preparation for the planned meeting between President Donald J. Trump and Kim Jong Un in the coming weeks."
After shaking hands over the Military Demarcation Line dividing the two Koreas, Kim stepped over -- making him the first North Korean leader to enter the South since the Korean War ended in armistice 65 years ago.
He and Moon Jae-in then momentarily stepped back over the line into the North, before setting off for their inter-Korean summit -- just the third of its kind since the war's end in 1953.
The encounter is intended to pave the way for a much-anticipated meeting between Kim and US President Trump.