The surprise meeting in a village on the North Korea side of the border was held to exchange opinions about holding a successful summit between Kim and President Trump and on how to implement steps that South Korean President Moon Jae-in and Kim agreed to in their last meeting on April 27.
It is unknown whether North Korea requested the meeting first, but sources told ABC News it was arranged in the morning.
President Moon is to announce details of the meeting at a press conference on Sunday, according to the presidential office.
Kim was with his sister Kim Yo-jong and his top aide Kim Yong chol in charge of inter-Korean affairs. Moon was accompanied by South Korea’s national intelligence service chief, Suh Hoon.
The statement by Seoul’s Blue House on Saturday came hours after Trump tweeted that the summit could still happen on June 12 as previously planned.
ABC News’ Kate Lee and Nataly Pak contributed to this report.