The Taliban renewed threats Wednesday to kill its remaining 19 Korean hostages if their demands were not met but did not immediately set a deadline.

“If the demands of the Taliban are not met, the Korean hostages face death,” said purported rebel spokesman Zabihullah Mujahed to Agence France-Presse by telephone from an unknown location.

“Although we want this crisis to be solved through negotiations, it seems the U.S. authorities are creating problems,” he added.

Mujahed also reported that most of the captives were sick from weather conditions and from lack of “proper food.”

“Their health condition is not good,” the spokesman said. “The weather conditions and a lack of proper food have made conditions for them very hard. Most of them are sick.”

Talks between Taliban negotiators and a South Korean delegation had initially appeared to be making headway when two female hostages were released last Monday. However, the negotiations have since become deadlocked with the rebels continuing to demand the release of its jailed fighters in exchange for the Koreans.

South Korea has explained that it has no power to concede to the rebels’ demand as the prisoners are held by the Afghan and U.S. military.

Both Kabul and Washington have stated from the beginning that they will not release any prisoners because it will only encourage future terrorism and kidnapping in a country already struggling with violence and lawlessness.

After a second round of face-to-face talks that began last Thursday, the Taliban said Saturday that the negotiations had “failed” and on Monday said it was losing patience with the South Korean delegation. Despite this, the Taliban and South Korea have still been holding talks over the telephone.

“We’ve been in phone contact with the Korean delegation,” Mujahed confirmed. “So far, there has not been any decision for face-to-face talks.”

According to Yonhap news agency, the Afghan government has set up a presidential committee to move forward negotiations on the crisis. The committee consists of representatives of the foreign affairs, interior and national security ministries.

It has been over a month since the Taliban militants abducted the group of 23 South Korean Christian volunteers on July 19 – the largest abduction of foreigners in Afghanistan since the fall of the Taliban regime in 2001. During that period, two male hostages have been killed – the leader of the group, Bae Hyung-kyu, who was found dead on July 25, and 29-year-old Shim Sung-min, whose body was found July 30.

Last week, the rebels released two females – 37-year-old Kim Kyung-ja and 32-year-old Kim Ji-na – as a “gesture of goodwill” when talks were going well.