Also Wednesday, suspected Taliban militants ambushed and shot to death five Afghans working on a U.S.-funded project to help end opium farming in the south of the country, officials said.
The man, who called himself Temur Shah, has also had negotiations with aid group CARE International — the employer of hostage Clementina Cantoni — said CARE's Afghanistan director, Paul Barker.
"The guy, if he is who we think he is, has blood on his hand from previous incidents," Barker said. "It's very ugly, what kinds of threats he makes." He declined to elaborate.
Cantoni herself did not speak during the interview, and Shah did not give any proof that she was in his captivity.
On the private television station Afghan Tolo, Shah threatened to kill Cantoni, 32, if three demands were not agree to by Wednesday night.
"If our demands are not accepted ... we will show our reaction and finish her," he said.
He demanded that the government set up more Islamic boarding schools in Afghanistan, that authorities provide "alternative livelihoods" for farmers who are being forced to stop growing opium, and that independent radio station Arman stop broadcasting a program about young people's social issues. He did not say why he opposed the show.