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.
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.”
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.”
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.