The country's Red Cross also wants to open talks of its own "to discuss restarting reunions between families separated by the Korean War", NPR's Elise Hu notes.
The last time talks between Seoul and Pyongyang took place, was in December 2015. South Korea's former President Park Geun-hye demanded that Pyongyang seriously commit to changing its nuclear program before talks between the countries would be held.
North Korea will likely accept Moon's proposed talks on easing border animosities, as it's something that it's previously called for.
There was no immediate response by the North to the proposal for talks later this week. The talks would be held next week at the Demilitarized Zone on the Korean Peninsula.
The majority have died without having had the opportunity to review.
The armed conflict between both countries ended with a cease-fire in 1953, but no formal peace treaty was ever signed, meaning the neighbouring countries technically remain at war.
The meetings of the families had begun in earnest after a historic summit in the North/South in 2000.More news: USA calls for smaller deficits in new NAFTA talks
Cho, whose office handles ties with the North, said South Korea does not have a hostile policy against North Korea and does not seek North Korea's collapse or unification through absorption. But this strategy has for the moment been douchée by the acceleration of the nuclear and missile programs in Pyongyang. Pyongyang has been under United Nations sanctions since 2006, when the Security Council demanded that it cease nuclear testing and banned the provision of large-scale arms, nuclear technology and related training to Pyongyang.
This test, which is closer to Pyongyang of its objective, which is to be in a position to threaten the u.s. territory of the nuclear fire, has led to strong condemnations around the world and new efforts from the White House to toughen the global sanctions.
The price of gasoline sold by private dealers in Pyongyang and the northern border cities of Sinuiju and Hyesan jumped to $2.18 per kg ($2.92 per liter) as of July 5, up 50 percent from $1.46 per kg on June 21, according to Reuters analysis of data collected by the Daily NK website.
The proposed meetings could, if they occur, constitute "a rare opportunity to ease the tensions that have been rising since 10 years", said Cheong Seong-Chang, of the Institute Sejong, a think tank.
Trump said unless China exerts its pressure on North Korea, the US will have to take unilateral action.
The proposed meeting would aim to end "all acts of hostility" along the border.