Taliban demand UN protection if talks take place in government-controlled area.
Two hostages have been shot dead since the group was seized and the Taliban has said that more captives will be killed unless some of their fighters are released from jail, a demand the government has rejected.
The remaining hostages are said to be seriously ill.
On Saturday, the AFP news agency reported it has received a phone call from a woman, purported to be one of the 21 hostages.
“If that doesn’t work, then force may be used,” he said.
Chun Ho-sun, the South Korean presidential spokesman, said: “Through our contacts, our foremost goal is to make it clear that there is a limit as to what our government can do to meet their demands of releasing the prisoners.”
The Afghan government has refused to release prisoners in exchange for the hostages and the US has said it will “not make concessions to terrorists”.
A German engineer and four Afghans kidnapped a day before the Koreans are also still being held by the Taliban, who are demanding Germany withdraw its 3,000 troops from Afghanistan. Berlin has flatly rejected the demand.