The soldier was in serious condition at a South Korean hospital on Wednesday following two rounds of surgeries.
The soldier was being operated upon for a second time on Wednesday, the hospital treating him said.
South Korean troops found the injured soldier south of the border after hearing sounds of gunfire, a South Korean Defense Ministry official said, requesting anonymity, citing department rules. In 1998, a North Korean solider fled to South Korea via Panmunjom.
President Donald Trump is now concluding his tour of Asia, which involved multiple discussions with regional leaders including Japenese Prime Minister Shinzo Abe, Chinese President Xi Jinping, and Filipino President Rodrigo Duterte regarding how to address the North Korean threat.
"We sent three of the largest aircraft carriers in the world (to the Korean Peninsula), and a nuclear submarine is also positioned", President Donald Trump said after his arrival last week in South Korea.
The Immigration office between South and North Korea, the only gateway leading to the Kaesong industrial park, was closed with red barricades blocking access to its premises in Paju, Gyeonggi Province, on November 1.
He has reportedly used it to stay in contact with North Korea's ambassador to the UN, Pak Song-il, in Pyongyang. The DMZ, created at the end of the 1950-53 Korean War, serves as a de facto border between the Koreas.
He received gunshot wounds to the shoulder and elbow from North Korean forces while defecting.
A South Korean Defense Ministry official said the three USA carriers held drills on either side of the waters separating the Korean Peninsula and Japan.
DiMaggio said that Trump has made possible attempts at negotiations with North Korean's harder because of his rhetoric and turmoil he faces in the U.S.
The 1984 exchange of gunfire happened after North Korean soldiers crossed the border and fired, according to the U.N. Command. While both sides of the DMZ are guarded by barbed wire fences, mines and tank traps, the JSA includes the truce village of Panmunjom which provides the site for rare talks and draws curious tourists. In Monday's incident, it wasn't known if the North continued firing after the defector was officially in the southern part of the Joint Security Area.
The presidency has changed since, from the former Park Geun-hye administration to the incumbent Moon Jae-in's, but the tension is continuing to build up with North's reluctance to denuclearize and come forward for dialogue.