Qari Yousef Ahmadi, who is said to speak for the Taliban, has said the Taliban are ready to negotiate anywhere, as long as the UN mission guarantees their safety.
Ahmadi had said earlier that the Taliban was ready to meet Kang Sung-Zu, the South Korean ambassador to Afghanistan.
He said: "The Taliban are ready to meet them in Kabul, other cities or other country, but only under one condition and that is that the UN guarantees their safety."
The Taliban have already killed two of the hostages, accusing the Afghan government of not negotiating in good faith and ignoring their demand to release prisoners. It has said it will kill the other hostages if its demands are not met.
The government has refused to release Taliban fighters for fear of encouraging kidnapping and after being criticised over a similar deal in March.
The hostages are said to be ill, but the Taliban have refused to allow Afghan doctors access to the group.
Amnesty International said on Friday it had appealed in a phone call to Ahmadi for the South Korean hostages to be freed, warning that holding and killing captives is a war crime.
Irene Khan, secretary-general of the London-based group, said in a statement: "Hostage taking and the killing of hostages are war crimes and their perpetrators must be brought to justice."
Ahmadi told Amnesty that "we are trying to resolve this issue ... acceptably," but did not agree to protect the hostages from harm, the statement said.
The South Korean government has called for "flexibility" in negotiations, but has not publicly called for the prisoners to be exchanged for the hostages.
On Thursday, eight senior members of South Korea's National Assembly travelled to Washington to urge US officials to take an "active and positive" approach to the crisis.
There is a widespread perception that Washington could influence Afghanistan's government.
The US has said it will not negotiate with groups it regards as "terrorists", but Richard Boucher, the US assistant secretary of state for South and Central Asian affairs, said on Thursday that "military pressure" was one of "many tools" available to resolve the crisis.
He said: "The goal is to get these people released unharmed, to get them released peacefully and safely."
Officials in Kabul have denied reports of a possible military operation to release the hostages.
The body of Shim Sung-Min, the second hostage to be killed, arrived at Seoul's Incheon airport on Thursday evening.
In Seoul on Friday, small protests were held outside some mosques, while about 24 Christian clergymen held a prayer service outside the US embassy in the South Korean capital, praying for the aid workers and urging the US to accept the Taliban's demands to secure the hostages release.
While some in South Korea blame the US for the situation, on the other side of a line of riot police a number of demonstrators staged a counter-protest.
"Do not use hostage situation to incite anti-US sentiment," one placard read.