According to the Yonhap News Agency, the 21-year-old private first class was still alive when he was found but succumbed to his wound at about 5:38 p.m. local time (08:00 GMT) on the way to a hospital.
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An investigation is set to be launched into the incident.
The relations between Seoul and Pyongyang have been showing signs of detente since the beginning of 2018. In January, North Korea reopened a border hotline with the South that had been closed for almost two years, while on April 27, South Korean President Moon Jae-in and North Korean leader Kim Jong-un met at the Panmunjom truce village, where they signed a joint declaration agreeing to renew economic cooperation in several areas.