"I was awake all night and if the Taliban had killed any of them I would have known," said General Ali Shah Ahmadzai, provincial police chief of Ghazni province where the 22 remaining hostages are being held and where one was killed on Wednesday.
The Taliban said the Afghan government had been given until late Wednesday night (2030 GMT) to agree to exchange the group for eight imprisoned rebels, but the deadline passed without word from the kidnappers.
"No, they have not killed any of the hostages and we are trying to contact the Taliban for resumption of talks," the Ghazni police chief told Reuters.
No Taliban member could be contacted for comment.
Earlier reports by some media that eight hostages had been released have been denied by officials, negotiators and a spokesman for the Taliban.
The fate of the 22 Christian volunteers had hung in the balance overnight, after the rebels shot dead one hostage and dumped his bullet-ridden body near where the group was seized last week.
He was identified in Seoul as the group's leader, Bae Hyung-kyu, a pastor who would have turned 42 on the day he was murdered.
South Korea's government strongly condemned the Bae's murder, calling it an unforgiveable atrocity.
"The government and the people of South Korea condemn the kidnapping of innocent civilians and the atrocity of harming a human life," said Baek Jong-chun, presidential Blue House chief national security adviser.
"Harming innocent civilians can never be justified and we will never forgive this kind of inhumane act," he said in a nationally televised statement.
