The bullet-ridden body of Bae Hyung-kyu was found last Wednesday, the day he would have turned 42. Bae was the leader of a group of 22 other volunteers kidnapped by the Taliban earlier this month.
His brother, Bae Shin-kyu, told reporters the family would not have a funeral until the other hostages were returned to South Korea.
The victim Bae, married with a 9-year-old daughter, was a founding member of the Saemmul Church south of Seoul, which sent the volunteers to Afghanistan.
Taliban leaders said on Sunday their fighters would kill the 22 remaining South Korean hostages if the Afghan government did not release rebel prisoners by a new deadline of 0730 GMT on Monday, a spokesman said.
Sporadic talks between the Afghan government and South Korean diplomats on one side and Taliban rebels on the other have continually snagged over the rebel demand for Kabul to swap jailed insurgents for the Koreans.
