Trump tweets Kim Jong-un an invitation to meet in DMZ
Trump made the offer on Twitter, hours before he was due to visit Seoul from Osaka, Japan, where he has been attending a Group of 20 summit.
"After some very important meetings, including my meeting with President Xi of China, I will be leaving Japan for South Korea (with President Moon)," Trump wrote.
"While there, if Chairman Kim of North Korea sees this, I would meet him at the Border/DMZ just to shake his hand and say Hello(?)!"
There had been speculation that a Trump-Kim meeting could happen inside the Demilitarized Zone when he visits Seoul on Saturday and Sunday.
But Trump denied before leaving Washington on Wednesday that he planned to meet Kim, saying only that he may speak to the North Korean leader "in a different form."
If the two meet, it will be their third time seeing each other after their historic first summit in Singapore last June and their second summit in Vietnam in February.
The U.S. and North Korea have been negotiating the dismantlement of Pyongyang's nuclear weapons program in exchange for sanctions relief, but talks have stalled since the second summit ended without a deal.
An exchange of personal letters between Trump and Kim this month led to hopes for a revival of talks.