PARIS — Algerian extremists allied with the Islamic State group have decapitated a French hostage after France carried out airstrikes in Iraq, according to a video that appeared online today.

French President Francois Hollande condemned the killing of Herve Gourdel and said France would continue its fight against the Islamic State group, which are Sunni militants that have taken over large swaths of Iraq and Syria.

“Herve Gourdel is dead because he is the representative of a people — ours — that defends human dignity against barbarity,” Hollande said, speaking at the U.N. General Assembly meeting in New York. “We will continue to fight terrorism everywhere.”

A group calling itself Jund al-Khilafah, or Soldiers of the Caliphate, had said they would kill the French mountaineer after abducting him Sunday unless France ended its airstrikes against Islamic State fighters in Iraq within 24 hours.

France started airstrikes in Iraq on Friday, the first country to join the U.S. military campaign against Islamic State fighters there.

The killing of a hostage represents a departure for radical Islamic groups in Algeria, which in the past decade have made millions off ransoming hostages. France is also known for paying ransoms.