North Korea on Thursday rejected a proposal from the South that the reunions take place during the Lunar New Year, citing South Korea's annual joint military exercises with the United States, Yonhap News Agency reported.
On Friday, South Korea urged the North to reconsider and take steps toward improving inter-Korean relations.
"We urge North Korea to show a sincere attitude toward our offer," said Unification Ministry spokesman Kim Eui-do.
Meanwhile, the North indicated that the reunions may take place in "a good season," and called for talks on resuming South Korea's tour program to Mount Kumgang, a mountain resort on the east coast of North Korea.
The South suspended the tours in 2008 when a South Korean tourist was fatally shot by a North Korean soldier. The tours were a major source of revenue for the North.
Kim said discussions on restarting the tours could happen, but separately from talks on reunions.