South Korean officials have begun their first face-to-face talks with Taleban militants on the fate of 21 Christian hostages, Afghan officials say.
Two men who were part of the group of hostages have already been killed
The talks were being held in the city of Ghazni, a senior official in the province told the BBC.
The official said he was optimistic about the outcome of the talks.
Two of the South Korean hostages have been killed, and the Taleban say they will kill more of them if a number of militants are not released from prison.
Earlier the Taleban said the Afghan government had provided a written promise of safe passage to two of their top leaders, so that they could attend the talks.
"At 6:15 pm today the face-to-face talks between the South Korea delegation and a two-member Taleban team started in the city of Ghazni," Taleban spokesman Yousuf Ahmadi told the AFP news agency.
Another Taleban official earlier said there would be "no problem" for the hostages as long as the talks continued.
19 July: 23 South Korean Christian aid workers seized on bus in Ghazni province
26 July: Body of hostage Pastor Bae Hyung-kyu is found
31 July: Second hostage Shim Sung-min, 29, found shot dead
10 August: South Korean officials and Taleban start talks
The original group of 23 South Koreans - most of them women - were seized on 19 July as they travelled by bus on the main road from Kabul to Kandahar.
Two men in the group, including the leader, were killed by their captors within the first fortnight of captivity.
The Afghan government, stung by criticism over a previous prisoner exchange, has ruled out a swap to secure the release of the Koreans.
Officials say military force could be used to free the group if the talks fail.
The South Korean government has repeatedly said it is opposed to direct military action.
It is thought the South Korean aid workers are being held in a number of small groups in a village about 10km (six miles) from Ghazni city centre.