Yousuf said that if a prisoner exchange is not met, more Koreans could be executed. The leader of the group was killed earlier in the week.
Baek Jong-Chun, a South Korean presidential envoy, arrived in Afghanistan for an urgent meeting with Hamid Karzai, the president.
Al Jazeera's James Bays said the government had imposed a media blackout. He said the Taliban had claimed to have struck a deal with the authorities for eight of its imprisoned members to be released.
Song Min-Soon, foreign minister, said on Thursday that Seoul would make "every possible effort" to secure the release of the hostages.
The Afghan government had not confirmed a prisoner deal reached, but authorities previously had publicly refused to swap prisoners for the hostages.
The deadline extension came as one of the 22 Korean hostages was allowed by the Taliban to give an interview to a local news agency.
A woman, who identified herself as Yo Syun-ju, told an Afghan journalist by telephone that all the hostages were sick and pleaded for help to secure their release.
Yo, who said she was from Seoul, described her situation as "dangerous," and said: "Day by day it is getting very difficult ... We are all sick and we have a lot of problems."
Watch Al Jazeera's report on the hostages' families
Ahmadi confirmed that some of the South Koreans were not in good condition.
"I don't know if the weather is not good for them or our food. The women hostages are crying. The men and women are worried about their future."
The Koreans, including 18 women, had been split into small groups and were being fed bread, yogurt and rice,
Qari Yousuf Ahmadi, a Taliban spokesman, said.
The Taliban spokesman said Major General Muhammad Munir Mangal, deputy interior minister of Afghanistan, contacted the Taliban and said the government would make a decision regarding their demands by the noon Friday deadline.
Ahmadi said: "The Taliban are not asking for money. We just want to exchange our prisoners for Korean hostages ... When they release our prisoners, the Taliban will release the hostages."
Roh Moo-hyun, the South Korean president, spoke to Karzai on Thursday, and they agreed to fully co-operate on freeing the remaining captives, Roh's office said.
"The Taliban are not asking for money, we just want to exchange our prisoners for Korean hostages"
Qari Yousif Ahmadi, Taliban spokesman
But Seoul also said it opposed the launch of a military operation to try to free them.
Ali Shah Ahmadzai, police chief of the Ghazni province where the Koreans were captured, said Afghan negotiators were speaking with the Taliban over the phone in efforts to secure their release.
Ahmadzai said: "We will not use force against the militants to free the hostages ... The best way in this case is dialogue."
Despite calls for negotiation, Afghan police and army units remained mobilised in large in Ghazni' Qarabagh district, where authorities believe the hostages are being held in a number of locations.
South Koreans in Seoul have been attending Friday prayers in remembrance of the murdered hostage, and in hope that the other hostages will be returned safely.
Sulaiman Lee Haeng Lae, the Imam at Seoul's Central Mosque, said: "We strongly ask for the release of the Korean hostage immediately and appeal for help to bring them back home safely, as well as ask for the support of all Muslims across the world."
On Wednesday, the Taliban killed one of the hostages. Afghan officials confirmed they had recovered the bullet-riddled body of Bae Hyung-Kyu, a Presbyterian pastor and the leader of the South Korean group.
The Taliban claimed responsibility for the killing, accusing the Afghan government and South Korean negotiators of failing to act in good faith after they rejected an initial list of eight Taliban fighters to be freed from prison.
|The Taliban killed Bae, pictured, the leader of|
the held South Korean group [AFP]
"Since Kabul's administration did not listen to our demand and did not free our prisoners, the Taliban shot dead a male Korean hostage," the Taliban's spokesman said.
South Korea has condemned the Taliban for the killing of Bae.
Baek Jong-chun, the chief national security adviser, said on Thursday: "The government and the people of South Korea condemn the kidnapping of innocent civilians and the atrocity of harming a human life."
"Harming innocent civilians can never be justified and we will never forgive this kind of inhumane act," he said in a nationally televised statement.
Bae, who was killed on his 42nd birthday, was co-founder of the Saem-Mul church which sent the volunteers to Afghanistan. He had a wife and nine-year-old daughter.