KABUL, Afghanistan — A purported Taliban spokesman said Saturday that the Islamic militia had killed two German hostages, a claim disputed by both Afghanistan and Germany. He also offered to trade 23 captive South Koreans for imprisoned Taliban fighters.

The militant spokesman offered no proof of his claim on the kidnapped Germans. Afghan officials said one of the Germans appeared to have died from a heart attack, while the other was still alive.

“Everything indicates he was a victim of the stress of the kidnapping,” German Foreign Minister Frank-Walter Steinmeier said in Berlin.

Despite the competing claims, the separate seizures of the foreigners in southern provinces were vivid illustrations of the lack of government control over the region.

Qari Yousuf Ahmadi, who claims to speak for the Taliban, said the Afghan and South Korean governments had until Sunday evening to agree to release 23 Taliban militants or the Korean hostages would be killed.

“If the government of Afghanistan and the government of Korea are asking for the release of their hostages, then we believe the Taliban also have the right to ask for the release of their prisoners who are spending time in Afghan jails,” Ahmadi told The Associated Press by satellite phone from an undisclosed location.

It is not clear that Afghanistan would agree to such a deal. In March, President Hamid Karzai authorized the release of five Taliban prisoners in exchange for a kidnapped Italian reporter, but he called the trade a one-time deal. Karzai was also criticized by the United States and European nations who felt that trade would encourage more kidnappings.

Ahmadi claimed the Germans and five Afghans kidnapped along with them were shot to death because Germany did not withdraw its 3,000 troops from Afghanistan as demanded by the Taliban. The seven were kidnapped Wednesday in the southern province of Wardak while working on a dam project.

The Afghan government said it had information to the contrary.

“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.”

He did not reveal the source of the information or say anything about the Afghan hostages.

The South Koreans were kidnapped at gunpoint from a bus Thursday in Ghazni province 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.