The official refused to provide more details.
KCNA said the Yongbyon nuclear facility, which the North expressed a willingness to take offline if the United States takes corresponding action, "is a core one for its nuclear program".
The move was agreed upon during a meeting last month in Pyongyang by the leaders of the two Koreas, Kim Jong Un in the North and Moon Jae-in in the South.
The JSA is the only area along the 155-mile long demilitarized zone, or DMZ, where troops from both countries are face to face.
They have already dismantled propaganda loudspeakers and some guard posts along the border.
Demining projects are also set to begin on Monday in Gangwon province in South Korea's east, to allow teams to search for the remains of soldiers killed in the war, the ministry added.
The troops began removing mines on the southern part of the two sites.
South Korea would find itself more vulnerable to North Korean infiltration and assault via land routes, while North Korea would worry about front-line soldiers and residents escaping to the South more easily, Lee said. It is believed that there are tens of thousands of landmines in the two areas to be cleared. In 2015, a landmine blast blamed on North Korea maimed two South Korean soldiers and pushed the Koreas to the brink of war.
Moon, a liberal who aspires to improve ties with North Korea, is a driving force behind U.S.
North Korean leader Kim Jong Un (L) and South Korean President Moon Jae-in (R) cross back the military demarcation line to the south side after Moon crossing the border to north upon meeting for the Inter-Korean Summit April 27, 2018 in Panmunjom, South Korea.
North Korea recently asked for "corresponding" reciprocal measures for the possible dismantlement of its important Yongbyon nuclear complex, a demand experts say might refer to declaring an end to the war or easing sanctions imposed on its regime.
In a summit in April, the leaders of South and North Korea agreed to cooperate in declaring an end to the war this year, saying that they will seek multilateral talks involving the U.S. and possibly China. Past rapprochement efforts were often stalled after an worldwide standoff over the North's nuclear ambitions intensified. -North Korean nuclear diplomacy. It also comes as U.S. Secretary of State Mike Pompeo is set to visit North Korea's capital this month to try to set up a second summit between Kim and President Trump. But Trump, Pompeo and other US officials have recently reported progress in the denuclearization discussions with the North. Pompeo is to make his third trip to North Korea soon for talks. Forensic identification tests in Hawaii confirmed they belong to South Korean war dead, according to Seoul's Defense Ministry.