The agenda may also include the idea of stationing 35 troops each from the two Koreas in the JSA for joint security operations.
The agreement between the nations - which are technically still at war - was reached at a meeting in Pyongyang last month between South Korean President Moon Jae-in and his North Korean counterpart Kim Jong-un.
On Monday, units of South Korean army engineers with demining equipment were deployed to the border village of Panmunjom and another frontline area called "Arrow Head Hill" where the Koreas plan their first joint searches for soldiers killed during the 1950-53 Korean War.
The troops in the JSA used to be allowed to freely move across the military demarcation line (MDL) before the 1976 "axe murder incident" in which North Korean soldiers killed two US soldiers who were trimming a tree in the DMZ.
A spokesman said the operation had begun on both sides, though this was not confirmed by the North.
There was no immediate confirmation from North Korea that its troops had begun the process.
Many experts say the fate of inter-Korean deals can be affected by how nuclear negotiations would go between the United States and North Korea.
The development comes amid renewed worldwide diplomacy on North Korea's nuclear weapons program after weeks of stalemated negotiations.
"The DPRK is taking substantial and crucial steps to implement the joint statement made at the DPRK-US summit, but the US is still trying to subdue someone by resorting to sanctions", the unnamed commentary accused.
In November 2017, North Korean troops at the JSA shot one of their soldiers defecting to the South five times.
At Panmunjom, the Koreas are to spend 20 days clearing mines before withdrawing troops, weapons and guard posts in the area over the next five days.
Propaganda loudspeakers and some guard posts along the border have already been dismantled.
North Korea has called on the USA to actively engage in talks on declaring an end to the Korean War, which was halted in 1953 with an armistice, not a peace treaty.
Moon defended the agreements in remarks Monday on South Korea's 70th Armed Forces Day.
South Korean troops have gradually taken over most operations along their side of the border but global forces under the US -led United Nations Command retain major roles, especially at the JSA, where an American commander and a South Korean deputy lead the security battalion.
The KCNA said North Korea has taken "substantial and crucial steps" to implement the summit agreement with the United States but that Washington is still talking about intensifying sanctions, rather than trying to resolve the end-of-war declaration issue that should have been resolved decades ago.