The South Korean hostages were abducted from a bus travelling from Kandahar to Kabul on Thursday.
They are reportedly Christians on an evangelical and aid mission. At least 15 are said to be women. A Taleban spokesman said on Sunday that they were in good health.
The Taleban say they want to swap the 23 men and women for jailed fighters and are also demanding that South Korean forces leave Afghanistan.
Earlier, Gen Mohammad Zahir Azimi, a spokesman for the Afghan defence ministry, told the BBC: “We have surrounded the area. We haven’t launched an attack right now and we are assessing the situation.”
A spokesman for Nato forces said it was unaware of an operation but was ready to help the Afghan and South Korean governments if asked.
The seizure is the largest-scale abduction of foreigners since the fall of the Taleban regime in 2001.