After days of silence following an initial proposal from Seoul last week, Pyongyang said it would be willing to participate in a meeting on Wednesday or Thursday at the border truce village of Panmunjom.
"We welcome that the North has finally come forward to discuss the reunion," Unification Ministry spokesman Kim Eui-Do told reporters.
"Given the urgency of the matter, we will make preparations to hold the reunion as soon as possible," Kim said, adding the ministry would notify Pyongyang which day it preferred for the Panmunjom meeting.
Millions of Korean families were left separated by the conflict that sealed the peninsula's division.
Most family members have since died without ever meeting or talking to their relatives. Cross-border visits, along with postal and phone communications, are banned for ordinary citizens.
About 71,000 people - more than half aged over 80 - are on the South's waiting list for a reunion opportunity.
Last week, South Korea proposed holding the event on February 17-21 at the North's Mount Kumgang resort.
Around 100 people from each side would take part and, if it goes ahead, it would be the first such reunion since 2010.
Seoul had also called for immediate working-level talks to hammer out the logistical details, and some officials expressed frustration over the Lunar New Year weekend that the North was taking so long to respond.
A reunion was planned for last September but Pyongyang cancelled at the last minute. There are concerns it may do the same this time around, due to planned joint South Korea-US military drills likely to begin late this month.
The drills by the two allies are held every year but are routinely condemned by the North as a rehearsal for invasion.