Al Qaeda says it has beheaded a French hostage in reprisal for France's military intervention in Mali, according to reports.
Its North African arm claimed responsibility, Mauritania's ANI news agency reported, citing a commander for the group.
A French foreign office spokesman said they were trying to verify the report of the killing of Philippe Verdon, adding that "we don't know at the moment" whether it is reliable.
In a telephone call to the news agency, the group spokesman said Mr Verdon had been beheaded on March 10 "in response to the French military intervention in the north of Mali", ANI reported.
The AQIM commander described Mr Verdon as a French spy and said France's President Francois Hollande "bore the responsibility for the remaining hostages".
Mr Verdon and another Frenchman, Serge Lazarevic, were kidnapped from their hotel room on November 24, 2011, in the northern Mali town of Hombori.
Their families denied that the two men were mercenaries or secret service agents.
The killing, if proved true, would be a worrying development for Mr Hollande.
Another 14 French hostages are detained in Western Africa, including seven believed to be held in the Sahel region by al Qaeda in the Islamic Maghreb (AQIM) and its affiliates.
In August last year a video showing Mr Verdon describing the "difficult living conditions" was released on a Mauritanian website.
The hostages' families have in recent weeks expressed growing fears for their loved ones in the light of France's military actions in Mali.
Earlier Tuesday, Mr Verdon's father Jean-Pierre, complained that the families were hearing nothing from the French authorities.
"We are in a total fog and it is impossible to live this way," he told RTL radio. "We have no information."
Asked about France's refusal to pay ransoms to kidnappers, he replied that the families had no say in such "decisions of state".
Terror chief Mokhtar Belmokhtar, an AQIM leader and one of the world's most wanted men, had pledged revenge and vowed to attack western targets in Africa after France launched a campaign to help the country's embattled government drive Islamist militants out of northern Mali.
France now has more than 4,000 troops on the ground in Mali.
It launched a nine-week assault in January to dislodge the group and other Islamist militants who had hijacked a Tuareg rebellion in Sahel and seized the northern half of the country.
They were driven out from the main cities of Gao, Timbuktu and Kidal, after which some 1,600 French and Chadian troops began searching for Islamist rebels in their pocket hideouts in the mountainous region of northern Mali.
When asked by the ANI news agency whether Belmokhtar had been killed, the AQIM commander neither denied nor confirmed it.
There have been conflicting reports on whether he was killed in the French military campaign against the rebels.
Soldiers from Chad fighting Islamists in Mali had claimed to have killed Belmokhtar, who is said to have been the mastermind behind the recent Algerian hostage crisis at a remote gas facility in the Algerian desert.
The one-eyed gangster, nicknamed Mr Marlboro because of his involvement in cigarette smuggling, had also been dubbed "The Uncatchable" by French intelligence after being linked to a series of kidnappings of foreigners in north Africa over the past decade.
France has been carrying out DNA tests to determine whether militant leaders Belmokhtar and Abdelhamid Abou Zaid are among those killed in recent fighting in Mali.