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 ill.
The hostage issue is likely to cast a shadow over two days of security talks between Hamid Karzai, the Afghan president, and George Bush, his US counterpart, due to take place at Camp David in the US later on Sunday.
The presidents are also expected to discuss the increasing number of civilian casualties sustained during military operations in Afghanistan, as well as the country's booming poppy trade.
A South Korean delegation travelled to Ghazni last week seeking face-to-face meetings with the kidnappers to try to break the deadlock, but there has been no agreement on where to hold direct talks.
On Saturday, the AFP news agency reported it has received a telephone call from a woman, purported to be one of the 21 hostages.
"I don't want to die. We want to go home," she said in English. "I don't know how long we can survive."
The South Koreans, a group of church volunteers who were undertaking aid work in Afghanistan, were snatched from a bus in Ghazni province on July 20.