North Korea has proposed reunions of families separated since the Korean War six decades ago.
The proposal is part of a campaign of reconciliation that included a call for the South and the US to cancel joint military drills.
South Korea welcomed proposal, which North Korea offered to hold "at the South's convenience" in a message received and made public by the South's Unification Ministry on Friday.
But the two sides have been at this stage before, either going ahead with or calling off the brief, highly choreographed reunions, only for the North to return to its bellicose rhetoric within days.
In September, the North abruptly cancelled the reunions just days before they were to take place, dealing a setback to months of efforts to improve ties and, according to the South, "breaking the hearts" of ageing Koreans who had to hoped to see their long-lost relatives for one last time.
North Korea at the time accused the South of using the events to promote conflict. The South called the cancellation inhumane and "deeply regrettable".
The two Koreas remain technically at war, as their 1950-53 civil conflict ended in a truce rather than a peace treaty. The war left millions of families divided, with private travel across the border and communication including phone calls banned.
The reunions, if they take place, would mean a resumption after a break of more than three years. Separated families meet for fleeting moments at a resort in Mount Kumgang just north of the Korean border.
South Korea has said the reunions should be held more frequently on humanitarian grounds.
Tensions soared earlier last year as Pyongyang reacted angrily to tightened U.N. sanctions imposed in response to its latest nuclear test.
South Korea-US military drills
The North sharply criticised the joint military drills conducted annually by the South and the United States and accusing them of being a prelude to war.
Sin Son Ho, North Korea's ambassador, said that the international community should no longer allow the US and South Korea to carry out the military drills on the Korean peninsula, which are scheduled for February and March.
"If the 'coordination' and 'cooperation' with the US are so precious and valuable, they had better hold the exercises in the secluded area or in the US far away from the territorial land, sea and air of the Korean peninsula," Sin said.
The North has traditionally called for the joint exercises to be called off, seeing them as a prelude to invasion. Sin repeated that demand at the UN on Friday, first made by North Korea last week, for the drills to be canceled.
South Korea 17 rejected on January the North's call to halt military drills, saying that as a democracy, it does not launch pre-emptive strikes.
The drills have been conducted for decades with a major incident and the two allies have stressed that they are purely defensive in nature aimed at testing readiness against North Korean aggression.