An AQIM statement said the killings on Saturday were in response to France's "new crusade", Sahara Media reports. AQIM said their killing was intended to avenge "crimes" committed by French and African troops against the people of northern Mali, Sahara Media, a news agency based in Mauritania, reported on its Arab-language website.
"The organisation considers that this is the least price that President Francois Hollande and his people will pay for their new crusade," AQIM's statement said.
French troops drove Islamist groups out of northern Mali's main towns after launching an offensive in January.
France described the killing of Ghislaine Dupont and Claude Verlon as a "calculated assassination".
Ms Dupont, 57, and Mr Verlon, 58, worked for Radio France International (RFI).
They were kidnapped and shot dead on Saturday after interviewing a local leader in the northern town of Kidal.
They were grabbed by four armed men in a four-wheel-drive vehicle at around 1 p.m. on Saturday. Their bullet-riddled bodies were found 12 kilometers (7 miles) outside the city, a few yards from the kidnappers' vehicle, whose steering wheel appeared to be broken, according to a senior Malian intelligence official who insisted on anonymity because he was not authorized to speak on the matter.
The Sahara website identifies the al Qaeda leader who carried out the killings as Abdelkarim al-Targui, one of the few Malian nationals who has risen to prominence inside the al Qaeda branch, led almost exclusively by Algerian jihadists, reports Associated Press
Targui is a native of the Kidal region and is believed to be responsible for the previous kidnappings of two French nationals, Philippe Verdon and Serge Lazarevic, who were grabbed from the town of Hombori in northern Mali in 2011. Lazarevic remains in captivity. Verdon was executed earlier this year.
There are 200 French troops and 200 African peacekeepers as well as a Malian army base in Kidal.
The bodies of the journalists have been repatriated to France.
France's Foreign Minister Laurent Fabius has said operations are ongoing to find their attackers.
On Monday, Malian police officials said a number of suspects had been arrested in connection with the murders.
The French government could not confirm than anyone had been detained.
(With agency inputs)