Al-Qaeda in the Islamic Maghreb (AQIM) killed the two French journalists who were abducted in Kidal in north Mali, a website used by the group has said.An AQIM statement said the killings on Saturday were in response to France's "new crusade", Sahara Media reports.
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".
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.
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.
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.