The Taliban commander also rejected an Afghan government claim that a senior leader, Mullah Brother, was killed in a US-led operation on Thursday in the southern province of Helmand.
An official in South Korea's presidential office said on Saturday:"We deny any payment for the release of South Korean hostages."
"The two conditions for the release are that we pull out our troops and stop Korean missionary work in Afghanistan by the end of the year," said the official, who declined to be named.
Rangeen Dadfar Spanta, the Afghan foreign minister, earlier criticised Seoul for negotiating with the Taliban, saying it set a dangerous precedent that could lead to more kidnappings.
Song Min-Soon, the South Korean foreign minister, said the country had no choice about negotiating with the Afghan group while the lives of the 19 remaining hostages were at stake.
"The government struggled to strike a balance between the international norms and custom concerning this kind of issue and the absolute premise that we have to save the people's lives," he said.
The South Korean Christian volunteers are due to fly to Seoul on Saturday after leaving Afghanistan on a chartered UN plane bound for Dubai the day before.
They were part of a group of 23 missionaries kidnapped in southeast Afghanistan in mid-July.
The Taliban killed two male hostages and released two women as a goodwill gesture.
Some of the 19 released hostages have told how they lived in constant fear for their lives and were split up into small groups and shuttled around the Afghan countryside to avoid detection.
One Taliban member would tend to a farm by day and then grab a rifle and stand guard over hostages at night, they said.
The kidnapping was the largest in the resurgent Taliban campaign against foreign forces since US-led troops removed the Islamists from power in 2001.
The Taliban decided to free the hostages after Seoul restated its plan to pull all its forces out of the central Asian country.
Seoul had already decided before the crisis to pull its 200 engineers and medical staff out of Afghanistan by the end of this year.
It has also banned nationals from travelling there.