Also Monday, the South Korean Red Cross Society proposed a meeting at Panmunjom on August 1 with its North Korean counterpart, to arrange reunions of relatives in the North and South who have not seen each other since being separated during the 1950-53 Korean War.
Tensions continue to escalate on the Korean Peninsula as North Korea conducts missile tests with increased frequency.
China views South Korea's offer to hold military and Red Cross talks with North Korea as "positive messages", Chinese Foreign Ministry spokesman Lu Kang said at a regular press briefing in Beijing on Monday.
Moon's government proposed two sets of talks to discuss how to dial down tensions and resume reunions of aging Koreans separated by the 1950-53 Korean War.
Seoul's Unification Ministry says these latest proposals are in line with President Moon Jae-in's dual track policy to pursue both engagement with the Kim Jong Un government while also supporting USA led sanctions to pressure Pyongyang to halt its nuclear and ballistic missiles programs.
The last such meetings were held in 2015, when fewer than 100 elderly Koreans from each side were allowed to spend three days with their family members.
While Cho says there is no "separation" between the USA and South Korea on dealing with the North Korean nuclear threat, Washington continues to emphasize pressure over dialogue and is preparing new sanctions on Chinese banks and firms doing business with Pyongyang possibly within weeks, according to US officials.
The proposed dialogue would be aimed at decreasing the tensions in the region.
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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 US President Donald Trump to impose harsher United Nations sanctions.
The two Koreas restarted Cold War-era psychological warfare after the North's fourth nuclear test in January 2016.
Washington has also called on China, the North's sole ally, to put more pressure on Pyongyang to curb its nuclear ambitions, which have advanced rapidly under leader Kim Jong-Un. The North will likely focus on blocking the cross-border spread of anti-Pyongyang leaflets by activists here.
Tongilgak is a North Korean building at the Panmunjom truce village on the border used for previous inter-Korea talks.
It was unclear how North Korea will react since it remains suspicious of new South Korean President Moon Jae-in's outreach to it.
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.
South Korea's new defence chief Song Young Moo, formerly a Navy chief, on Monday stressed the importance of a strong military power to support peace efforts.
The agenda for the military meeting could include moves to suspend propaganda campaigns operated on both sides of the border for years, Cheong added.