"There is no change in our position that we will put forth effort to (persuade) North Korea to come out for denuclearization by using all possible measures such as sanctions and talks", said South Korean Unification Minister Cho Myung-kyun.
If realized, the talks would be the first inter-Korean dialogue since December 2015. But the South's then-president, Park Geun-hye, a conservative who has since been impeached and removed from office, rejected the offer, calling it insincere and demanding that the North first move toward dismantling its nuclear weapons program.
If the talks are held, loudspeaker broadcasts, leafleting and South Korea-U.S. drills are expected to top the agenda. It was the Moon government's first formal proposal for talks with North Korea since its May 10 inauguration.
The Moon administration is eager to restart humanitarian assistance and exchanges despite no let-up in the North's provocations highlighted by its July 4 firing of a ballistic missile with intercontinental range.
North Korea is believed to possess hundreds of missiles capable of striking South Korea and Japan.
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. "There will be a response from North Korea".
The South Korean Red Cross on Monday also proposed holding talks in August with the North to arrange reunions of family members separated during the 1950-53 Korean War, with the hope of scheduling the reunions in October during the Korean Chuseok holiday.
Unveiling his peace vision in the German capital earlier this month, President Moon stressed the importance of dialogue to address the current situation, which he described as "highly dangerous". -South Korea military drills.
He called for a sweeping reform of the country's armed forces for a "new war paradigm", reported Yonhap news agency. But he still has not backed off from his outreach to North Korea, arguing during a recent speech that both Koreas must stop hostile activities along the border and resume family reunions.
Pyongyang, however, has demanded Seoul turn over 12 waitresses who defected to the South past year before it will agree to holding family reunions.
There are also reports of increased activity at the Yongbyon uranium enrichment facility that could indicate plutonium production underway in the previous year to further increase the North's nuclear weapons stockpile. South Korea has offered to talk with North Korea to ease animos.
In an act to rein in the North, the United States is preparing new sanctions on Chinese banks and firms doing business with Pyongyang possibly within weeks, two senior USA officials said last week.