SEOUL, South Korea — Reversing its earlier stance, North Korea on Friday agreed to a South Korean proposal to resume a long-suspended humanitarian program that arranges reunions of elderly relatives separated six decades ago by the Korean War.

President Park Geun-hye of South Korea raised the idea during a news conference on Jan. 6, suggesting that the reunions would be an important first step toward building trust and improving relations on the divided Korean Peninsula.

As recently as Jan. 9, North Korea had rejected Ms. Park’s overture. It said the political mood was not right, citing — among other things — the joint military exercises South Korea plans to hold with the United States from late February through April.

On Friday, however, North Korea suggested that a new round of reunions could take place in the tourist resort at Diamond Mountain in southeast North Korea, according to the North’s official Korean Central News Agency. It left it to the South to choose a date for the reunions “when the weather thaws.”