SEOUL, South Korea — South and North Korea agreed on Saturday to resume high-level talks this year, raising hopes for a thaw in the long-tense relations on the divided Korean Peninsula.

A statement from South Korea did not specify what would be discussed. But South Korea had proposed in August that senior officials meet to discuss a new round of reunions of family members separated by the Korean War six decades ago, a program that has proceeded in fits and starts for years as inter-Korean relations have fluctuated.

The North had rejected the August overture, insisting that Seoul first stop activists in the South from sending balloons into North Korea bearing antigovernment propaganda.

But a breakthrough appeared to come on Saturday, when top South Korean policy makers met with a North Korean delegation visiting Incheon for the closing ceremony of the Asian Games, a surprise visit that South Korea announced just an hour before the officials’ arrival. The delegation included three of the most trusted aides of the North Korean leader, Kim Jong-un.