There was no independent confirmation of his death.
 
The body of the hostage had been dumped in the Qarabagh district of the southern province of Ghazni, Ahmadi said.
 
The area is where 23 South Korean Christians, officially on an aid mission, were captured on July 19.
 
They were seized while they were travelling on the highway between Kabul and Kandahar, in Ghazni, about 140km south of the Afghan capital.
 
No comment
 
The South Korean embassy in Afghanistan has refused to comment to the media on the case.
 
James Bays, Al Jazeera's correspondent in Afghanistan, said: "They [the Taliban] have extended [the deadline] in the past, but they say they are serious this time."
 

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"If anything happens to them, the Afghan government and the South Korean government will be responsible."

Qari Yousef Ahmadi, Taliban spokesman

 
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He reported there was a build up of security forces in the area.
 
"There are a lot of troops and police in the area near the main highway where the South Koreans were kidnapped."
 
The leader of the group, Bae Hyung-kyu, a 42-year-old pastor, was shot dead on  Wednesday and his bullet-riddled body found in a desert area of the province.
 
Bae's body arrived in South Korea on Monday.
 
Melissa Chan, reporting for Al Jazeera from Seoul, said: "The family members have said that they will not hold a funeral until the rest of the hostages are back and safe."
 
Taliban denial
 
Earlier on Monday, Yousuf had denied that there had been any agreement to extend talks further.
 
"We are still awaiting the decision of the leadership council. We have not extended the deadline till Wednesday," he told Reuters by telephone from an unknown location.
 
Reports had said that the Taliban extended their "final" deadline at the request of Afghan mediators, but insisted that the release of Taliban prisoners was the only way to settle the crisis.
 
The "final deadline" was issued by the movement's leadership council on Sunday and orginally ran out at 0730 GMT.
 
Demands
 
The Taliban have demanded the withdrawal of South Korean troops from Afghanistan and the return of prisoners held by the Afghan authorities.
 
On Sunday, Yousuf said that the group's demands remained the same.
 
He said: "We have the same previous demands; the first is accepting to withdraw the Korean forces from Afghanistan."
 
"The second demand is still pending as the Afghan government delegation has said that it does not have the authority to release Taliban prisoners."
 
Hostage swap?
 
For their part, Afghanistan's interior ministry and the presidential palace have said a hostage swap is out of the question.
 
An Afghan team that was supposed to have held more talks with the Taliban on Saturday could not reach the group because of security concerns in Ghazni province, a provincial source said.
 
The Taliban has said that if anything happens to the South Korean hostages, "the Afghan government and the South Korean government will be responsible".

Source: Al Jazeera and agencies