Families separated since the Korean War will have the chance to see each other again in mid-February if North Korea agrees to the South's offer.
Seoul's unification ministry said it made the proposal through the inter-Korean hotline on Monday morning.
"Considering the wishes of the separated families, we proposed holding a round of family reunions at Mount Kumgang from February 17th to the 22nd, for six days."
The ministry also offered to hold working-level talks on Wednesday at the North Korean side of the truce village of Panmunjom to fine-tune the details of the event.
The North took many by surprise with its sudden proposal last Friday that the reunions resume at a convenient time for South Korea after the Lunar New Year holiday, which falls at the end of this week.
If the event takes place next month, 1-hundred divided family members from each side will be reunited.
Millions of Koreans were separated from their loved ones when the country was divided more than six decades ago.
Around 72-thousand South Koreans are on the waiting list for a chance to meet their families one last time, although time is running out for the very elderly relatives.
Despite the friendlier tone in recent weeks, preparations for the event may run into some problems due to the upcoming joint military drills between South Korea and the United States.
The South Korean government has made clear the drills will take place as scheduled, starting at the end of February, despite North Korea's repeated calls to cancel what it views as war games.
This year's training, however, will not involve U.S. aircraft carriers or strategic bombers.
Seoul is expected to notify its neighbors, including Pyongyang, of the schedule and purpose of the exercises after the Lunar New Year holiday.
Hwang Sung-hee, Arirang News.