France's prime minister said Tuesday his country won't stop fighting Islamic State militants despite demands by kidnappers holding a French hostage.

The 55-year-old man was abducted in Algeria on Monday by a splinter group from Al Qaeda's North African branch. The Jund al-Khilafah, or Soldiers of the Caliphate, said it would kill him unless France halts it airstrikes in Iraq within 24 hours.

Manuel Valls said Tuesday on Europe 1 radio that French authorities are "doing everything" to try to free the hostage, but won't negotiate with his captors.

"If we cede, if we retreat one inch, that would hand victory" to the militants, he said.

French forces on Friday joined the U.S. in carrying out airstrikes against extremists who have overrun large areas of Syria and Iraq.

Algerian authorities reported massive searches involving the army, gendarmes and village guards throughout the Djura Djura mountain range, part of the Kabylie region where Herve Gourdel was kidnapped.

A mountain guide in France, the Nice native was on a hiking trip with two Algerian friends when his car was stopped by militants Sunday night.

Algeria's once powerful Islamic extremists have been largely confined in recent years to a few mountainous areas, including the region Gourdel chose to hike in.

The U.S. embassy in Algiers renewed its travel warning for Algeria Tuesday, urging Americans traveling there to "exercise vigilance" in their movements.