KABUL, Afghanistan (CNN) -- Afghan Taliban rebels said Saturday they have killed two German hostages captured Wednesday, but the Afghan Foreign Ministry said one is still alive and the other died of a heart attack.
The militants also said they will start killing a busload of South Korean hostages, captured Thursday, if South Korea does not withdraw its troops from Afghanistan, according to Reuters news agency.
The rebels also are demanding the Afghan government release Taliban prisoners.
Asked about the Foreign Ministry statement on the status of the German hostages, a Taliban spokesman said the government is lying and that both men have been killed.
"Their time in this world is done," Taliban spokesman Zabiullah Mujahid told CNN. "The terms weren't met."
He said Afghans who accompanied the Germans are still alive, but provided no more details.
Another Taliban spokesman, Qari Yousuf Ahmadi, earlier said the first German was killed at 12:05 p.m. Saturday and the second an hour later.
"The second German was executed at 1:20 p.m.," Ahmadi said. "We waited an extra 20 minutes, but there was no contact from either the German government or the Afghan government. Therefore, we killed him as we said that we would."
But Afghan Foreign Ministry spokesman Sultan Ahmad Baheen said "our security agencies reported to us that one of the German engineers is still alive, and the second died of heart attack and heat."
He added that "our security forces are trying to secure the safe return of the German national who is still alive in the custody." He declined to say who the kidnappers were. Watch what government, Taliban officials are saying about the hostages »
"After today's work, we must assume that one of the kidnapped Germans died in captivity," said German Foreign Minister Frank-Walter Steinmeier. "Nothing points to murder. All signs tell us that he fell victim to the strain to which his kidnappers subjected him. ... Now it is essential we do our utmost and take full responsibility for saving the life of the second German hostage."
A Foreign Ministry spokesman said there is an "action committee" keeping "close contacts with the Afghan government and is continuing its intense efforts."
Meanwhile, in South Korea, President Roh Moo-hyun, in an address to his nation Saturday, called on the Taliban to free the South Koreans, who he said were in Afghanistan performing volunteer medical work. Mostly women, they are members of a Christian church.
The number of the hostages is unclear. The Taliban said 18 people were kidnapped. But the Korean government said 23 had been taken.
Roh said the 200 South Korean troops in Afghanistan are in the last phase of their noncombat mission to provide medical help and rebuild the country.
"Our government will do everything we can for their safe and quick return," he said of the hostages.
The South Korean foreign minister said his country already planned to withdraw its troops from Afghanistan by the end of this year. E-mail to a friend
CNN's Atia Abawi in Baghdad, CNN's Sohn Jie-ae in Seoul and journalist Thomas Coghlan in Kabul contributed to this report.