The hostages worked for Terre D'enfance, an agency working with children in Afghan's southwest.
The Taliban will give the French government another week to negotiate the release of a French man and three Afghans who were captured with her, Ahmadi said.
"We have extended the deadline for the French man and three Afghan hostages for another week," he said.
The woman, who has been named in the media only as Celine, was carrying a message to the French government that it must "cut its military assistance to Afghanistan," Ahmadi said.
Afghan police clashed with Taliban fighters on Saturday in eastern Afghanistan, and a subsequent Nato airstrike left 11 dead, officials said.
Three police were wounded in the fighting.
The police and Taliban engaged in a one-hour gun battle in the Alishar district of Khost province, said Wazir Padshah, a spokesman for the provincial police. He said Nato assisted with an airstrike, killing 11 people.
Angela Billings, International Security Assistance Force spokeswomen, confirmed that Nato launched a strike early on Saturday, causing some casualties.
She said there were no Nato or civilian casualties.