Abu Musab Abdel Wadoud, of Al-Qaeda in the Islamic Maghreb [AQIM], made the comments in an audio tape aired by Al Jazeera on Thursday.
Five French nationals and two Africans - employees of French companies Areva and Vinci - were kidnapped in Niger on September 16.
Abdel Wadoud also said that any negotiations over the release of the hostages should be carried out directly with al-Qaeda's leader, Osama bin Laden.
"The summary of the message is very clear," he said in the broadcast.
"You will not find security anywhere until we also have security and safety in Palestine, Afghanistan, Iraq, Somalia, the Maghreb and so on.
"If you don't stop intervening in our affairs and the oppression of Muslim people, and if you want peace for your citizens that we hold hostage, you must withdraw your forces from Afghanistan as soon possible according to a set timetable that you will announce publicly.
"If you reject this offer, you will be held responsible in the eyes of your people."
France said on Friday it was working to authenticate Abdel Wadoud's message. Bernard Valero, the French foreign ministry spokesman, told the AFP news agency that the recording "is being authenticated now".
He said that France was "fully mobilised" in an effort to secure the release of the five French hostages along with the Togo and a Madagascar nationals.
"For this kind of complex and delicate situation, discretion is an important part of our activity," Valero said.
Herve Morin, who was closely following the hostage crisis until losing his defence portfolio in last week's cabinet reshuffle in France, said that the reference to Bin Laden was new.
"Withdrawing French troops from Afghanistan is a kind of classic, traditional demand for all kinds of attacks," he told France Info radio.
"What's new is the reference to bin Laden. Generally, and particularly with AQIM, it's more of a franchise."
Last month AQIM offered to release the hostages in exchange for a repeal of the ban on the face veil in France, the release of fighters and €7m [$9.88m], according to a report by Al Arabiya television.
Bin Laden had said in an audio tape also aired on Al Jazeera last month that the kidnapping was prompted by France's unjust treatment of Muslims.
Source:Al Jazeera and agencies