The soldier was in serious condition at a South Korean hospital on Wednesday following two rounds of surgeries.
A local police agency, which took custody of the man from the military, said Wednesday it will send him to the immigration office for deportation.
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.
"It could be assessed the U.S. efforts and approach toward North Korea are producing a degree of results", Lim told the National Assembly's Foreign Affairs and Unification Committee on Friday, referring to the hiatus in North Korean provocations since September 15. "The military is maintaining a full readiness", the Joint Chiefs of Staff statement said.
Coupled with security issues, talks of the possible establishment of a direct US-North Korea dialogue channel are expected to be on the agenda.
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.
REUTERS US President Donald Trump says Kim Jong Un's North Korea is a"hell that no person deserves
Trump said in Seoul that it makes sense for North Korea to come to the table and "make a deal", saying that he has seen "a lot of progress" in efforts to make Pyongyang give up nukes.
Two North Korean soldiers came over to the South in June after crossing the frontier.
About 30,000 North Koreans have defected to South Korea since the end of the 1950-53 Korean War, but most travel through China.
The JSA is jointly overseen by the American-led U.N. Command and by North Korea, with South Korean and North Korean border guards facing each other only meters (feet) apart. A North Korean soldier defected there in 1998 and another in 2007 but neither of those events involved gunfire between the rivals, according to South Korea's military. 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.
The senior diplomat added the U.S. was providing Seoul with sufficient information on the matter and that Trump's speech indicated Washington's acknowledgement of progress in dealing with North Korea issues. In 1976, North Korean soldiers axed two American army officers to death and the United States responded by flying nuclear-capable B-52 bombers toward the DMZ in an attempt to intimidate the North.