Qari Yousef Ahmadi, who claims to speak for the militants, said the Afghan government hadn't responded to any of its demands and that between 11:30 a.m. (0700 GMT) and 2 p.m. (0930 GMT) the militants would kill "a few" of the hostages.
"The Taliban have lost their patience with it all so they (the South Korean hostages) will be killed, 100 percent, because a lot of time has passed since the deadline and there has been no response," Ahmadi told The Associated Press by satellite phone. "The Taliban takes no responsibility for the killing."
Though some of Ahmadi's statements turn out to be true, he has also made repeated false claims, calling into question the reliability of his information.
Ali Shah Ahmadzai, the provincial police chief, said he thought talks had been on a positive track and said the new threat was a surprise.
"I don't know why they've suddenly changed their mind," Ahmadzai said. "My message to the Taliban is to use tolerance and be patient. This (killing hostages) is against the Afghan culture."
The South Korean hostages, including 18 women, were kidnapped last Thursday while riding a bus through Ghazni province on the Kabul-Kandahar highway, Afghanistan's main thoroughfare.
South Korean negotiators have traveled to Ghazni province to take part in the negotiations. Three previous deadlines for the hostages' lives have passed with no consequences.
In South Korean, Foreign Minister Song Min-soon told lawmakers that a "safe release may not be necessarily matched by a quick release."
He said the 23 Koreans are being held in different locations and that there are difficulties in negotiating to secure their release.
Song also said the South Koreans do not have any health problems. However, Seoul is pushing to send medical supplies to the captives.
He gave no further details.
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