In the interview, the woman pleads for help and says all of the hostages are sick.
CBS said it arranged the telephone interview with a Taliban commander.
Deadline Extended
The Afghan government, meanwhile, says Taliban militants have extended a deadline to negotiate the release of the hostages.
The French AFP news agency quotes Wahidullah Mujadadi, the head of the Afghan government delegation negotiating with the kidnappers, as saying the deadline is now noon local time July 27.
Mujadadi says the government is doing its best to win the hostages' release.
Officials in Seoul have condemned the killing on July 25 of one of its citizens by the captors -- a priest and leader of the Christian volunteer group.
The South Korean government called the execution "an unforgivable atrocity."
Foreign Ministry spokesman Cho Hee-yong said Seoul has renewed its calls for the Taliban to immediately release the other 22 South Korean nationals, who have now spent a full week in captivity in Afghanistan's central Ghazni Province since being taken from a bus on the Kabul-to-Kandahar highway.
The government in Seoul rejected earlier reports that some of the hostages had been released.
Senior Envoy Dispatched
In a telephone conversation today, South Korean President Roh Moo-hyun and his Afghan counterpart, Hamid Karzai, agreed to further cooperate toward the captives' safe and quick return, Roh's office said.
South Korea has dispatched a senior envoy -- Baek Jong-chun, chief presidential secretary for security affairs -- to Afghanistan to participate in the ongoing negotiations with the Taliban kidnappers.
Before departing for Afghanistan, Baek pledged that the kidnappers "will be held accountable for taking the life of a Korean citizen."