In Paris, a French Foreign Ministry official said the government is aware of the report and is investigating.
The Noukachott Information Agency, or ANI, posted the report late Tuesday. The ANI website is frequently used by al-Qaida's North African chapter to post messages. It was not possible to independently verify the execution claim.
ANI quoted a man who identified himself as Ghairawani, a spokesman for al-Qaida in the Islamic Maghreb, as saying the group's fighters had executed a French hostage, Philippe Verdon, on March 10.
Verdon was kidnapped with another Frenchman, Serge Lazarevic, from their hotel room in Hombori in eastern Mali in November 2011. Their families have said they were in the region to study setting up a cement factory there.
French troops launched a campaign in January to help Mali's embattled government drive Islamic militants out of northern Mali. The campaign has raised fears of retaliation against French hostages. Fifteen French citizens have been taken hostage in the region, among them a family of seven people including four children who were seized a month ago in Cameroon.