A jihadist group in North Africa aligned with the Islamic State claimed responsibility for the kidnapping of a Frenchman in a mountainous region of Algeria, hours after the Islamic State called for attacks on Westerners. In the video released Monday, the little-known group Jund al-Khilafah said France had 24 hours to halt attacks on the Islamic State, also known as ISIS, or see its citizen executed.

Manuel Valls, the French prime minister, said Tuesday that his government would not stop its campaign despite the threat.

He told Europe 1 radio that French authorities are “doing everything” to free the hostage, but will not negotiate with his captors. “If we cede, if we retreat one inch, that would hand victory” to the militants, Mr. Valls said.

The kidnapping was the first of a Westerner by an Islamic State-aligned group outside Syria. If copied, the tactic of kidnapping Westerners to pressure their governments could expand the conflict beyond the group’s current footprint, given that the Islamic State has secured pledges of allegiance from fighters in other regions of Africa and the Middle East, and elsewhere in Asia.