During the talks, the two presidents agreed not to carry out the springtime South Korea-U.S. joint military exercises, codenamed "Key Resolve and Foal Eagle", during the PyeongChang Winter Olympics.
The agenda would include North Korea's offer to send a delegation to the games, as well as overall inter-Korean relations, South Korea's Unification Ministry spokesman, Baik Tae Hyun, told reporters Friday.
A South Korean government official checks the direct communications hotline to talk with the North Korean side at the border village of Panmunjom, South Korea, January 3.
President Trump, who had engaged in a war of words and insults with Kim including saying that his "nuclear button" is bigger than the North Korean's, tried on Thursday to claim credit for the talks.
Reviving the nations' first formal dialogue in more than two years was another sign that animosities were easing after months of rising tensions over the North's nuclear and missile programs.
South Korean President Moon Jae-in and U.S. President Donald Trump have agreed not to conduct the joint war games between Seoul and Washington during the South Korea-hosted Winter Olympic Games slated to kick off in February, Moon's office said Thursday.
North Korea regularly threatens to destroy the United States and its two key Asia allies, Japan and South Korea, and says its weapons are necessary to counter USA aggression. This time, South Korea asked whether they had any news.
Friday's announcement came not long after USA and South Korea agreed to postpone one of the world's largest military exercises until after the Winter Olympics next month.
"They can talk with whoever they want", she said about North Korea, but made the U.S. requirements clear. "Is it one-off from him or a real olive branch?"
Commercial satellite imagery from December 25 showed a rail-mounted environment shelter had been moved away from a test stand, indicating that an engine test may be in the near future, the website said, rather than a new rocket launch suspected in recent media reports.
Worldwide sporting events have previously produced diplomatic openings between the two Koreas, only to lead nowhere.
Trump expressed his hope that the inter-Korean dialogue would bring a good outcome, telling Moon that the United States supports President Moon 100 percent.
The announcement of the planned talks came amid a series of developments on the Korean Peninsula. Officials in Beijing have sought to get the parties back to negotiations to reduce the risk of a USA military strike that could topple their longtime ally or draw them into a regional conflict.