In the South, troops began removing mines on the southern part of the two sites on Monday morning.
The other area being demined is around the so-called "Arrow Head Hill", where some of the war's heaviest fighting took place over a strategically important hilltop position.
However, he said this did not mean South Korea would accept North Korea as a nuclear state, suggesting Seoul's diplomatic efforts to halt the North's nuclear programme would continue.
But critics of his engagement policy have lambasted his recent inter-Korean military deals, saying a mutual reduction of conventional military strength would eventually weaken South Korea's war readiness because the North's nuclear program largely remains intact.
All the landmines in the Joint Security Area - the only portion of the DMZ where forces stand face-to-face - are expected to be removed within 20 days.
"It's the start of peace", said Kim Ki-ho, head of the private Korea Mine Clearance Research Institute.
The JSA is the only spot along a 250km long "demilitarised zone" (DMZ) where troops from both Koreas are face to face. "We have to remove those mines, though we are not taking out all the mines at the DMZ".
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He called for the United States to offer the expertise of the Federal Bureau of Investigation and top scientists to determine who was behind the attack.
The South's Defense Ministry says it detected North Korean soldiers engaging in what it believes are demining-related work at the two sites.
KCNA said that Pyongyang was willing to take "such. steps as eternal dismantlement" of its nuclear complex "if the USA takes a corresponding measure" but again did not elaborate. It is believed that there are tens of thousands of landmines in the two areas to be cleared.
At Arrow Head Hill, where some of the fiercest battles occurred during the Korean War, Seoul officials believe there are remains of about 300 South Korea and United Nations forces, along with an unspecified number of Chinese and North Korean remains.
Moon defended the agreements in remarks Monday on South Korea's 70th Armed Forces Day.
Apparently reflecting the improving ties, North Korea sent Choe Ryong-hae, its de facto No. 2 official, to a reception hosted by the Chinese embassy in Pyongyang last week to mark China's founding anniversary. They were earlier found in North Korea during a joint 1996-2005 excavation project between the United States and North Korea before forensic identification tests in Hawaii confirmed they belong to South Korean war dead, according to Seoul's Defense Ministry.
The development comes amid renewed global diplomacy on North Korea's nuclear weapons program after weeks of stalemated negotiations.
The Koreas' militaries agreed on a range of deals aimed at lowering their decades-long military animosities on the sidelines of a summit between their leaders in Pyongyang. Past rapprochement efforts were often stalled after an worldwide standoff over the North's nuclear ambitions intensified.
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