France said on Monday that a video of a kidnapped French family with their abductors, who claimed to be from Islamist extremist group Boko Haram, was a "shocking" display of the kidnappers' cruelty.

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"A video of the French family kidnapped last Tuesday in northern Cameroon has been released by Boko Haram," Foreign Minister Laurent Fabius said a in a statement. "For all of us, these images are terribly shocking. They display a cruelty without bounds."

The more than three-minute video shows the family, including four children, held in an undisclosed location, surrounded by at least three of the abductors from the Nigerian group whose faces are hidden.

A source close to the family confirmed their identities to AFP. It was not clear when the video was made.

Following the release of a video from the abductors French Prime Minister Jean-Marc Ayrault confirmed that Nigerian Islamist group Boko Haram had claimed responsibility for the kidnapping of a French family,

France "now has the information that Boko Haram claims to be holding" the seven French citizens kidnapped last week in Cameroon, Ayrault said after a top-level meeting following the release of the video on YouTube.

Ayrault said the family is "probably held in Nigeria".

"The video tape... is being studied by our (intelligence) services, who are examining precisely the nature of these claims," he said. "French authorities are in close and permanent contact with Nigerian and Cameroonian authorities."

Threats made to family

In the video one of the abductors speaks in Arabic while addressing Nigerian President Goodluck Jonathan. "If you want us to release these French citizens, quickly release all our women you are detaining," he said.

He calls on Cameroon to release "our brothers" and warns the group will kill its hostages if its demands are not met. At the start of the video, the father Tanguy Moulin-Fournier reads a statement from a piece of paper, his four children in front of him, his wife and brother beside him.

The family, with children aged five to 12, were kidnapped on February 19th in Cameroon.

Cameroonian authorities said the victims, who were visiting a national park at the time, were taken over the border into Nigeria's restive northeast after being abducted.

There was widespread confusion on February 21st, when  France was forced to deny a claim that the family had been freed. The French foreign ministry released a statement formally denying "the information that the French hostages had been released".

Earlier that day, a Cameroonian military source had told AFP the seven members of a French family who were seized had been found in northern Nigeria.

"The hostages are safe and sound and are in the hands of Nigerian authorities," the source said on condition of anonymity. "They were found abandoned in a house in Dikwa" in northern Nigeria, the source added.

The family's liberation was falsely reported throughout the French media.

A French minister came under fire for initially confirming the family's release to AFP, before backtracking immediately and declaring he could not confirm the family had been found.