Two female South Korean hostages have been freed by the Taliban on Saturday night, a purported Taliban spokesman Yousuf Ahmadi said.
The two sick hostages were freed unconditionally and were staying in Ghazni province, Ahmadi told Xinhua from an undisclosed place, adding soon they may reach Ghazni city, the provincial capital.
They were freed as the Taliban leadership wanted to show a " good gesture" toward South Korean authorities, he said.
The Taliban wanted to accelerate the talks on South Korean hostages by releasing the two females, he added.
However, neither Afghan nor South Korean officials have immediately confirmed the releasing.
Meanwhile, the Taliban spokesman Ahmadi said other hostages would not be released if the Taliban's demands for the liberty of some Taliban prisoners were not met, according to some media reports.
Several South Korean diplomats and two Taliban delegates, who are Mullah Bashir and Mullah Nasratullah, carried out first face- to-face talks on the hostages on Friday and Saturday in Ghazni city.
Earlier Saturday, the two Taliban delegates said the negotiations were going on very well, and hopefully the hostages would be released in one or two days if the Taliban's demands were met.
They also showed their optimism toward a peaceful end to the hostage crisis and assured all hostages would be released.
The Taliban said the two delegates were sent to the government- controlled city for the talks as Afghan authorities gave a written guarantee for their safety.
A total of 23 South Koreans were kidnapped by Taliban militants on a road in the central Ghazni province on July 19.
Taliban rebels killed two male hostages on July 25 and July 30 separately to press Afghan and South Korean authorities to meet their demands. The others were still being held by Taliban militants.
The Afghan government has refused to release Taliban prisoners as the Taliban has demanded to exchange for the hostages.
Taliban militants have carried out kidnappings in Afghanistan over the past two years frequently, and some hostages were killed.