There was no immediate response by the North to the proposal for talks later this week.
The two sides technically remain at war but Moon, who came to power in May, has pledged to engage the North in dialogue as well as bring pressure to impede its nuclear and missile programmes.
The offer comes after the North claimed to have conducted the first test of an Intercontinental Ballistic Missile (ICBM) on July 4.
The Norh also said it had mastered the technology to mount a nuclear warhead on the missile.
South Korea and the United States, its main ally, dispute the claim.
“Talks and cooperation between the two Koreas to ease tension and bring about peace on the Korean peninsula will be instrumental for pushing forth a mutual, virtuous cycle for inter-Korea relations and North Korea’s nuclear problem,” the South’s Unification Minister Cho Myoung-gyon told a news briefing.
The South Korean defence ministry proposed talks with the North on July 21 at Tongilgak to stop all activities that fuel tension at the military demarcation line.
Tongilgak is a North Korean building at the Panmunjom truce village on the border used for previous inter-Korea talks.
The last such talks were held in December 2015.
Cho also urged the restoration of military and government hotlines across the border, which had been cut by the North in 2016 in response to the South imposing economic sanctions after a nuclear test by Pyongyang.
In all, the North has conducted five nuclear tests and numerous missile tests.
The South also proposed separate talks by the rival states’ Red Cross organizations to resume a humanitarian project to reunite families separated during the 1950 to 1953 Korean War in closely supervised events held over a few days.
The South Korean Red Cross suggested talks be held on Aug. 1, with possible reunions over the Korean thanksgiving Chuseok holiday, which falls in October.
The last such reunions were held in October 2015 during the government of Moon’s predecessor under a futile push for reconciliation following a sharp increase in tension over border incidents involving a landmine blast and artillery fire.