South Korea did not specify the exact location of the guard post but said it was somewhere in the "central frontier", which is on the eastern side of the demilitarized zone around the South Korean province of Gangwon.
There's a "low possibility" that the shots fired by North Korea were intentional, according to the South Korean military.
"Yesterday, Kim was trying to show he is perfectly healthy, and today, Kim is trying to mute all kinds of speculation that he may not have full control over the military", Choi said.
The exchange of gunshots on Sunday was the latest confrontation between the two Koreas that technically remain still at war after their 1950-53 conflict ended in a truce, not a treaty.
"Our military, through the military communication line, is taking actions with the North to figure out the situation and also to prevent additional actions from taking place, while maintaining military readiness", the Joint Chiefs of Staff said.
"The UNC will conduct a thorough investigation tomorrow to determine if there was an Armistice Agreement violation, and will provide the report to the appropriate authorities once completed". Lee Peters said in a statement.
An estimated two million mines are peppered inside and near the DMZ, which is also guarded by barbed wire fences, tank traps and combat troops on both sides.
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Trump has continued to refer to Kim as a friend, but the mystery of the past three weeks has served to emphasize the limits of that relationship and his lack of progress in persuading North Korea to give up a weapons program that now threatens the United States.
Trump on Saturday welcomed the leader's return.
"North Korea has in the past conducted calculate military provocations in the DMZ", Mintaro Oba, a former State Department official specializing in the Koreas, wrote on Twitter. "Unclear what exactly has happened/is happening at the moment".
"The explanations for an incident like this in the DMZ could range from accident/miscalculation at a local level to a bigger tactical decision in North Korea to heighten inter-Korean tensions to gain negotiating leverage", he added.
A senior South Korean presidential official on Sunday brushed off rumors that Kim had undergone surgery during his absence, saying they had enough grounds to believe he had not.
The incident occurred a day after North Korean state media reported Kim's visit to a fertilizer plant on May 1, his first public appearance in 20 days.
Mr Kim earlier vanished from the public eye after presiding over a Politburo meeting of the ruling Workers' Party on April 11 to discuss the coronavirus. There has been a lot of work in the last two years to ease tensions between the two countries after President Moon Jae-in met Kim Jong-un.