"We set several deadlines and the Afghan government did not pay attention to our deadlines," spokesman Yousuf Ahmadi told Agence France-Presse. "Finally tonight at 8:30 we killed one of the Koreans named Sung Sin with AK-47 gunshots."
Earlier, the deadline for the lives of the remaining 22 South Korean Christians held hostage in Afghanistan was extended to Wednesday, after their Taliban captors let pass two deadlines set for Monday.
Marajudin Pathan, the governor of Ghazni province, where 23 South Korean Christians were abducted on July 19, said the Taliban agreed to extend its deadline until Wednesday to allow time for additional negotiations over the Taliban prisoners' release.
He reported that authorities had talked to the Taliban on Sunday and asked for two more days of talks.
"Fortunately, they did not reject our demand outright, but said that they need to talk to their leaders," Pathan said early Monday, according to The Associated Press.
It has been over a week since Taliban militants abducted 23 South Korean Christians, including 18 women, in insurgency-prone Ghazni province. The church group was on their way to provide free medical services to poor Afghan citizens when their bus was hijacked last Thursday.
Since the abduction - the largest abduction of foreigners in Afghanistan since the fall of the Taliban regime in 2001 - one hostage has been killed. The leader of the aid group, Bae Hyung-kyu, was found dead last Wednesday with 10 bullet holes in his body.
Although the kidnappers have threatened to kill the remaining captives if their demands are not met and have reported that some of them were in poor health, Afghan officials have said they are optimistic the hostages will be freed without further bloodshed.
"Today we are hopeful to get a good result because more and more elders have gathered from Ghazni," said Qarabagh police chief Khwaja Mohammad on Saturday, according to AP. "I hope the Taliban will listen to these negotiations now because they are neutral people - elders from around Qarabagh district."
On Saturday, Abdul Salaam Rocketi, a former Taliban member who is now part of the Afghan parliament, joined the negotiating team for the release of the hostages.
Ghazni officials said the respected elders and clerics would explain to Taliban militants that taking hostage is unacceptable in Islam and Afghan culture.
"A lot of people are involved today. Inshallah (if God wills it), they will not kill them," said Ghazni lawmaker Habib Rahman, according to AP.
Two days of meetings between elders of Qarabagh district in Ghazni and a delegation of senior officials from Kabul, had yielded no immediate results, however, prompting the Taliban to set another deadline to give their threats added weight.
"Since the talks between us, the Kabul administration and Korean government have reached deadlock and they are not honest ... hence, we will start killing the hostages if they do not start releasing our prisoners by tomorrow at 12 o'clock," purported Taliban spokesman Qari Mohammad Yousuf told Reuters by telephone from an unknown location when announcing Monday's 0730 GMT deadline.
The spokesman later extended the deadline again to 1130 GMT by the request of the Afghan negotiators. He couldn't immediately be reached for comment regarding the latest extension.
Afghan officials have said that negotiations with the Taliban have been difficult because the kidnappers give conflicting statements and demands. Some have called for the release of women hostages, others have demanded the exchange of rebel prisoners, while still others demand ransom money. They have also demanded South Korea withdraw its 200 troops from Afghanistan.
But the Taliban's "main demand," according to the purported Taliban spokesman, is the release of rebel prisoners in exchange for the South Korean hostages.
So far, however, Afghan authorities are refusing to release rebel prisoners after the government came under criticism in March for freeing five Taliban in exchange for an Italian reporter
"Our goal is to seek ways on how we can free the hostages without compromising our laws and regulations in regards with such cases," police chief Alishah Ahmadzai of Ghazni province said to AFP.
A deputy interior minister on Saturday told Reuters that force might be used if talks fail, but Taliban spokesman Yousuf warned against use of force, saying Sunday that "it will jeopardize the lives of the hostages and the Taliban will resist till the last gasp of their breath."
Several foreigners have been held this year by Taliban militants waging a deadly insurgency against the Western-backed government that replaced the hardline regime driven from power in late 2001.