Story highlights The minister's statement comes after rebels show video of kidnapped family

The family of seven was kidnapped in Cameroon

A masked spokesman says France has declared war in Islam

Boko Haram wants jailed members and their wives released

France will not negotiate with the Islamist rebels who kidnapped a French family in Cameroon, Defense Minister Jean-Yves Le Drian said Tuesday.

"We do not negotiate on these bases, with those groups," Le Drian said on French radio station RTL. "We will use all possible means to secure the release of hostages."

The radio announcement comes a day after rebels in Nigeria released a chilling video of the family that was abducted in neighboring Cameroon.

The seven-member family was flanked by armed fighters from the Boko Haram movement in the brief video. One of the captive men read a statement demanding that Nigeria and Cameroon free jailed members of Boko Haram, which is battling to establish Islamic rule in northern Nigeria, and their families.

"Meet all the demands we have mentioned, and if you leave out one of them, we will kill these hostages," the masked man says.

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The family -- a couple, their four children and an uncle -- were seized in a national park in remote northern Cameroon on February 19. Authorities in Cameroon said they were quickly spirited across the border into Nigeria.

"This is the first time there are children hostages," Le Drian said. "This is an unacceptable situation."

French Foreign Minister Laurent Fabius denounced the video Monday, saying, "All of the state services are mobilized to free our countrymen."

"For all of us, these images are terribly shocking. They demonstrate cruelty without limits," Fabius said in a statement.

The kidnapping has raised fears of Westerners being targeted by Islamist militant groups in Africa in the wake of the French military intervention against other Islamist rebels in Mali. The masked man in the video says French President Francois Hollande "started war against Islam, and we must fight him everywhere."

The father works for the French company GDF Suez and is based in Yaounde, the capital in southern Cameroon. GDF Suez, which is developing a natural gas liquefaction project in Cameroon, said it was working closely with the French Foreign Ministry.