A portrait of mountain guide of Frenchman Herve Gourdel hangs near a French flag outside the town hall in Saint-Martin-Vesubie, September 24, 2014. Algerian militants have released a video that appears to show them beheading Gourdel who was kidnapped on S
A portrait of mountain guide of Frenchman Herve Gourdel hangs near a French flag outside the town hall in Saint-Martin-Vesubie, September 24, 2014. Algerian militants have released a video that appears to show them beheading Gourdel who was kidnapped on SundayReuters

Algerian extremists with affiliation to the Islamic State group have decapitated a French hostage after France apparently didn't heed to their warnings against carrying out airstrikes in Iraq, an online video shows.

French President Francois Hollande strongly condemned the brutal killing of Herve Gourdel and said that the attack will only reinforce the war against the Islamic State that is currently under way.

"Herve Gourdel is dead because he is the representative of people that defends human dignity against barbarity," Hollande said in New York where he was attending the UN General Assembly meeting. "My determination is total and this attack only reinforces it. We will continue to fight terrorism everywhere."

The caliphate soldiers, ISIS-linked militants, had earlier released a threat video online, claiming responsibility for the kidnapping of the French citizen. The video shows Gordel, a 55-year-old from Nice in southern France, with the militants warning that they would kill him if France did not halt its intervention in Iraq.

In the video, Gourdel mentions his name, age and date of birth. He arrived in Algeria on 20 September and was taken hostage the very next day, various reports have said. The footage was released by the group 'Jund al-Khilifa (Caliphate Soldiers), which has pledged its allegiance to the self-proclaimed Islamic State.

"I am in the hands of Jund al-Khilifa, and Algerian armed group. This armed group is asking me to ask you (President Francois Hollande), to not intervene in Iraq," Gourdel had said in the video. "They are holding me as a hostage and I ask you Mr. President to do everything to get me out of this bad situation and I thank you."

President Hollande on Wednesday described the killing as a "cruel and cowardly act" adding that the French air strikes, which began on IS targets in Iraq last week, would continue.

"France is going through an ordeal through the murder of one of its citizens, but France will never give in to blackmail," he told the UN General Assembly.

"The fight against terrorism must continue and be stepped up."

"We will continue to fight terrorism everywhere, notably against the group we call Islamic State, which spreads death in Iraq and Syria, pursues civilian populations, persecutes religious minorities, rapes, beheads," he said.