A Taleban spokesman says a South Korean from a group of 22 held hostage by the Taleban in southern Afghanistan has been killed.
The office of the governor of Ghazni province and local police also told the BBC the killing had taken place, but neither had seen the victim's body.
The Korean Christian aid workers were kidnapped 10 days ago.
The leader of the group was shot by the Taleban on Wednesday. The militants want government prisoners released.
"We set several deadlines and the Afghan government did not pay attention to our deadlines," said Taleban spokesman Qari Yousuf Ahmadi.
The al-Jazeera Arabic TV station showed footage of several of the hostages held by the Taleban.
Several women were seen in the footage with headscarves and Taleban militants in the background.
According to reports, no new deadline for the government to release its prisoners has been set by the Taleban.
The Afghan government is doing all it can to secure the release of the South Koreans, President Hamid Karzai said on Sunday.
He assured a South Korean envoy everything possible was being done to free the hostages - mainly women.
Mr Karzai said kidnapping foreign guests was "shameful", un-Islamic and against Afghan culture.