The appeal echoed comments by the South Korean president's office, after Afghan officials found the body of Shim Sung-min, 29, a former information technology worker who was a volunteer with the church group.
"The majority of the hostages are ill, but two females are seriously ill and there is this possibility that they may die," Yousuf said.
He said the two were suffering from an unknown illness and the Taliban did not have the right medicines to treat them.
The Afghan government has refused to free Taliban prisoners, saying it would only encourage further abductions.
The hostages – 16 women and seven men – were kidnapped while on a bus.
Douglas Shin, a South Korean pastor, told Al Jazeera: "They did their preparation for the trip. But they could have had a lower profile than using a tourist bus to travel the Kabul-Kandahar road."
US help urged
Earlier, South Koreans had urged the US to help free the remaining hostages as they mourned the death of a second captive.
Kim Jung-ja, the mother of one of the remaining captives, said: "We appeal for support from the people of the United States and around the world for resolving this crisis as early as possible.
"Especially, the families want the United States to disregard political interests and give more active support to save the 21 innocent lives."
In an apparent reference to the US
policy of not negotiating with anyone it deems terrorists, the South Korean president's office said: "The government is well aware of how the international community deals with these kinds of abduction cases.
"But it also believes that it would be worthwhile to use flexibility in the cause of saving the precious lives of those still in captivity."
The Taliban had extended several previous deadlines without consequences, but killed Shim Sung-min on Monday after a deadline passed. The group's pastor was killed last week.
A South Korean civic group criticised the US for refusing to get more involved in the standoff, saying it was as if the US was watching "a fire across a river".
The group also questioned what South Korea had earned for its alliance with Washington in its anti-terrorism campaign. Seoul has sent troops to Afghanistan and Iraq.
The Afghan government explicitly said for the first time on Tuesday that it would not release Taliban prisoners – the group's chief demand to free the captives.
Humayun Hamidzada, a spokesman for Hamid Karzai, the president, said: "As a principle, we shouldn't encourage kidnapping by accepting their demands."
In March, Karzai authorised the freeing of five Taliban fighters for the release of an Italian reporter, but called the exchange a one-time deal.
Tom Casey, a spokesman for the US state department, said there was regular contact between US and South Korean officials on the standoff, but would not comment on specifics.
Afghan judges killed
In a separate development, the bodies of four Afghan judges kidnapped nearly two weeks ago have been found in the same province where Taliban fighters are holding the South Koreans.
A photographer for Agence France-Presse, the French news agency, said he had seen the bodies of the four men.
|The bound feet of two of the judges [AFP] |
He said one had been shot in the head, the others in the body, and that their feet had been bound.
Police said the bodies had been dumped in a village in the southern Ghazni province.
The Taliban had claimed to have kidnapped the four but did not immediately confirm it was responsible for their murder.
Mohammad Zaman, a deputy police chief, said the men were judges from the neighbouring province of Paktika.
He said: "They were killed and their bodies were found in Dehyak district last night."
Source: Al Jazeera and agencies