"We make the proposal for a meeting ... aimed at stopping all hostile activities that escalate military tension along the land border", the defence ministry said in a statement.
The dialogue was created to hold a reunion event of families, who have been separated since the 1950-1953 Korean War ended in armistice, on the occasion of the Chuseok holiday in early October.
"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", Cho said.
Elected in May 2017 with promises of engagement, Moon reiterated his preference at the G20 summit in Hamburg in early July for dialogue with the north despite its "nuclear provocation".
If the government meeting goes ahead, it will mark the first official inter-Korea talks since December 2015. During a speech in the capital of a reunited Germany this month, Moon repeated his openness to direct talks with the North Korean leader on everything from weapons programs to outright peace.
But Pyongyang has staged a series of missile launches in violation of United Nations resolutions, most recently on July 4 when it test-fired its first ICBM, a move which triggered global alarm and a push by President Donald Trump to impose harsher United Nations sanctions on the country.
Cho stressed that Seoul "would not seek collapse of the North or unification through absorbing the North" and urged Pyongyang to restore inter-Korea communication channels, including a shuttered military hotline.
The South Korean Red Cross suggested talks be held on August 1st, with possible reunions over the Korean thanksgiving Chuseok holiday, which falls in October this year. Prospects for talks on family reunions are less good because North Korea has previously demanded that South Korea repatriate some North Korean defectors living in the South before any reunions take place, according to the analysts. But his push has reported little progress with the North test-firing a series of newly developed missiles since Moon's May 10 inauguration.
Novak said the military talks would be held first.
Washington has also called on China, the North's sole ally, to put more pressure on Pyongyang to rein in its nuclear ambitions, which have advanced rapidly under the North's leader, Kim Jong-un.
If the meeting is to take place as planned, it would be the first dialogue between the military authorities of the two sides in nearly three years; their previous meeting was held on October 15, 2014.