Yousuf Ahmadi, a Taliban spokesman, said the South Korean hostages, seized on Thursday, will be killed unless an equal number of Taliban prisoners are freed by Sunday.
Ahmadi also said that five Afghan engineers abducted alongside the two Germans have also been killed.
Roh Moo-hyun, South Korea's president, said on Saturday that Seoul is ready to make sincere efforts to win an early release of its citizens and that the Taliban "should send our people home quickly and safely".
The outlawed Afghan group is demanding the immediate withdrawal of German and Korean troops from Afghanistan and the release of all its members in Afghan prisons.
Ahmadi, speaking by telephone, said: "We executed one of the Germans and will kill the other one unless the government of Germany or the Afghan government contact us for negotiations at 1pm (08:30 GMT) today."
An hour and a half later, he said: "Since the governments did not contact us, we killed the second German hostage at 1:10pm."
However, Sultan Ahmad Baheen, an Afghan foreign ministry spokesman, later said: "The information we have is that one of them has died of a heart attack and the other one is still alive."
He cited Afghan security sources and said that the Taliban spokesman did not have credible information.
A spokeswoman for the German foreign ministry said that Berlin had received no clear evidence that the two Germans were in the hands of the Taliban.
|Taliban have warned US and Nato forces |
against forcibly trying to free the hostages
She said a special crisis task force at the ministry was working closely with the Afghan government to secure the release of the hostages.
In a newspaper interview on Saturday, Angela Merkel, the German chancellor, rejected the Taliban demand.
"We can't give up our efforts now," she was quoted as saying in an interview with Passauer Neue Presse newspaper. "The Afghan people can't be abandoned."
South Korea has reiterated its plans to withdraw troops from Afghanistan by the end of the year, as scheduled.
While Seoul has no combat troops in Afghanistan, it has a military contingent of about 200 engineers and doctors deployed in the war-torn nation.
Song Min-soon, South Korea's foreign minister, said he had spoken to his Afghan counterpart and that officials from both countries were working to secure the Koreans' release.
He said a team would leave for Afghanistan later on Saturday, and that the Afghan side had already set up a special task force to deal with the case.
Ahmadi warned the Afghan government and US and Nato forces not to try to rescue the hostages, or they would be killed.
The provincial police chief in Ghazni province said his forces were working "carefully" to not trigger any retaliatory killings.
The Taliban has said it is aware of the statements of the government of South Korea - that it will pull out its troops at the end of the year - but a Taliban spokesman told Al Jazeera that it is not good enough.
James Bays, Al Jazeera's correspondent in Kandahar, said: "They want to see the troops withdrawn, either immediately or in the next few days."
The spokesman also said that the Taliban believes that the South Koreans are missionaries.
The Taliban has seized a number of foreign nationals as part of its campaign to overthrow the Afghan government and drive out its Western backers.
Source: Al Jazeera and agencies