A purported Taliban spokesman said the hard-line militia killed two German hostages on Saturday because Germany didn't announce a troop withdrawal from Afghanistan.
The Afghan government, however, said one of the Germans died of a heart attack and that the second was still alive.
South Korea's government, meanwhile, attempted to win the release of at least 18 Korean Christians, including 15 women, kidnapped in the same region on Thursday.
Qari Yousuf Ahmadi, who claims to be a Taliban spokesman, said fighters had fatally shot the Germans, who were kidnapped on Wednesday along with five Afghan colleagues in the southern province of Wardak while working on a dam project.
"The German and Afghan governments didn't meet our conditions, they didn't pull out their troops," Ahmadi told The Associated Press by telephone from an undisclosed location.
Ahmadi offered no proof of the killings and said the Taliban would give further information about the two bodies later.
The Afghan Foreign Ministry said he was lying.
"The information that we and our security forces have is that one of these two who were kidnapped died of a heart attack," Foreign Ministry spokesman Sultan Ahmad Baheen said. "The second hostage is alive and we hope that he will be released soon and we are trying our best to get him released."
German Foreign Ministry spokesman Martin Jeager said a crisis team was pursuing "every clue" and was in close contact with the Afghan government.
Ahmadi said that 18 kidnapped Koreans would also be killed Saturday if South Korea didn't withdraw its 200 troops in Afghanistan.
South Korean President Roh Moo-hyun urged the Taliban to "send our people home quickly and safely." He said 23 South Koreans had been abducted.
Roh also spoke with Afghanistan President Hamid Karzai and asked for cooperation to quickly win the release of the South Koreans, Roh's office said.
A senior Korean official said the South Korean government was "maintaining contact" with the Taliban.
The South Koreans were kidnapped at gunpoint from a bus in Ghazni province's Qarabagh district on Thursday as they traveled on the main highway from Kabul to the southern city of Kandahar. It was the largest-scale abduction of foreigners since the fall of the Taliban regime in 2001.
Ahmadi warned the Afghan government and U.S. 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.
"We have surrounded the area but are working very carefully. We don't want them to be killed," said Ali Shah Ahmadzai.
Germany has 3,000 soldiers in NATO's International Security Assistance Force, are stationed in the mostly peaceful northern part of Afghanistan. South Korea has 200 soldiers in the U.S.-led coalition who largely work on humanitarian projects such as medical assistance and reconstruction work.
"We are doing whatever we can to secure their release, and we hope that those who have kidnapped them will respect the Afghan and Islamic culture not to harm them and let them go back to their homes safe and sound," Baheen said.
In South Korea, family members of kidnapped victims urged the government to accept the Taliban's demand, noting Seoul had already decided to bring home its soldiers by the end of this year.
"We hope that the immediate withdrawal (of troops) is made," Cha Sung-min, a relative of one of the hostages, told reporters.
South Korea's troops run a hospital for Afghan civilians at the U.S. base at Bagram, and the facility has treated over 240,000 patients. The kidnapped civilians are not affiliated with the military.
South Korean Foreign Minister Song Min-soon reiterated Seoul's plans to withdraw its troops from Afghanistan by the end of this year as scheduled, hoping to appease the militants.
"The government is in preparations to implement its plan," he said.