(CNN) -- A second South Korean hostage held captive by the Taliban in Afghanistan has been killed, a spokesman for the militant group told CNN on Monday.
Relatives of the kidnapped South Koreans await news about them on July 30.
The body was dropped off in Chardiwal in the province of Ghazni in central Afghanistan, Taliban spokesman Zabiullah Mujahid said in a telephone interview.
He identified the victim as Soon Shineen.
But the district governor of Qara Bagh, Khawaja Mohammad Siddiqi, said no body had been discovered at the location given by the Taliban.
The announcement came hours after Taliban leaders had threatened to kill more of the 22 Korean hostages they have been holding if Afghan leaders did not give in to their demands to release rebel prisoners.
Taliban spokesman Qari Mohammad Yousuf said the Taliban, who had already killed one hostage, would begin killing the others if the Afghan government did not act.
The Afghan government has ruled out a prisoner swap and has urged the Taliban to release the women being held.
The 23 South Koreans -- members of a church group in Afghanistan to perform volunteer medical aid -- were kidnapped 11 days ago from their bus in Ghazni province.
One of them -- Bae Hyung-Kyu, 42, a pastor at the church attended by the hostages and the leader of their group -- was shot and killed.
Police in southeastern Ghazni province found Bae's bullet-riddled body in the Qara Bagh district, where the Koreans were kidnapped on July 19.
Since then, the Taliban have announced a number of new deadlines that have passed.
Meanwhile, one of the hostages spoke by phone with CBS News and the BBC.
Identifying herself as Yo Syun-Ju of Seoul, the woman told the BBC to "tell them to do something to get us released."
"We want from the Koreans, from the U.N. and human rights people to exchange us, and that they do this," she said. "We are all sick and we have a lot of problems."
The same woman told CBS, "We are in a very difficult time. Please help us."
"We are all pleading for you to help us get out of here as soon as possible," she said. "Really, we beg you."
She said the hostages were being held in two groups, one of 17 women and the other of five men. E-mail to a friend
-- CNN's Atia Abawi contributed to this report from Baghdad.
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