Taliban kidnappers shot dead a South Korean hostage and threatened to kill 22 others unless their demands were met by 2030 GMT on Wednesday, a Taliban spokesman said.
A local government official confirmed the death.
"Yes, they have killed one of the hostages and efforts are under way to have the others released," district chief of Qarabagh in Ghazni province, Khowja Seddiqi, told Reuters.
The Taliban accused the Afghan government and South Korean negotiators of failing to act in good faith after they rejected a list demanding eight named rebel prisoners be freed.
"Since Kabul's administration did not listen to our demand and did not free our prisoners, the Taliban shot dead a male Korean hostage," Qari Mohammad Yousuf told Reuters by telephone from an unknown location.
"If the administration of Kabul is not ready to release our hostages, then by 1 am (local time) the rest of the hostages will be killed," he said. "That time is the last deadline."
He said the Korean hostage had been killed in a desert area in the Qarabagh district of Ghazni close to where the 23 Korean church volunteers -- 18 women and five men -- were abducted on the main road south from Kabul last week.
He rejected Korean media reports that said the Taliban planned to free eight of the captives.
Afghan President Hamid Karzai has pledged not to swap prisoners for hostages after being criticised at home and abroad for releasing five Taliban from jail in March in exchange for an Italian reporter.
But the president and ministers have remained silent throughout the latest hostage ordeal.
RELATIVES CRY
The kidnappings have made travel outside major cities risky for the thousands of foreign aid workers and U.N. staff in Afghanistan and may weaken support for military involvement among the more than 30 nations with troops in the country.
The abductions come amid 18 months of rising violence in Afghanistan with daily clashes between Taliban insurgents and Afghan and foreign troops, and a rise in suicide attacks and roadside bombs increasingly extending into areas previously considered safe.
A NATO soldier was killed on Wednesday in a rocket-propelled grenade attack in eastern Afghanistan, the alliance said.
Anxious family members of the Korean hostages gathered at the offices of a non-governmental agency in Seoul to follow developments on television. Sounds of crying emerged when news came out that one of the hostages had been killed.
Around 1,000 people gathered in suburban Seoul around Saemmul church, which sent the volunteers to Afghanistan, to pray for their safe return, broadcaster YTN reported.
Elsewhere in Afghanistan, a German journalist reported kidnapped earlier denied he had been abducted.
But another German and four Afghans seized last week are in Taliban captivity. The body of a second German with the group was later found with gunshot wounds.
Germany has refused the Taliban demand that it withdraw its 3,000 troops from Afghanistan.
