Pierre Legrand, Daniel Larribe, Thierry Dole and Marc Ferret were working for the French firms Areva and Sogea Satom in Arlit, northern Niger when they were abducted in September 2010.
On Tuesday, AQIM accused France of dragging its feet in a four-minute video message broadcast on the Mauritanian website Sahara Médias.
“A year ago, we notified France we were open to negotiate, [and] we are still waiting for a response,” says Abdel Hamid Abu Zeid, one of the leaders of Aqim, according to a transcript of the video.
He added the hostages are still alive.
In response, the French foreign ministry says French authorities “continue to demand our compatriots held in the Sahel be freed safe and sound,” and that everything is being done to achieve this.
“No stone has been left unturned,” the ministry’s statement added.
The French foreign minister, Laurent Fabius, has previously said the government is working “in discretion” to secure their release.
AQIM is also holding two French geologists, Philippe Verdon and Serge Lazarevic, who were kidnapped in Mali in 2011.
A seventh Frenchman, Gilberto Rodriguez Léal, was taken by Mujao, a militant group with links to AQIM, in November this year.
The latest kidnapping linked to AQIM was last week’s abduction of Francis Collmup, a 63-year old taken in northern Nigeria by Ansaru, a group with links to AQIM and the Nigerian militants Boko Haram.