Jihadists linked to the Islamic State group beheaded a Frenchman abducted in Algeria in a video posted online Wednesday, but President Francois Hollande vowed France would not give in to blackmail.

Hollande said the "cruel and cowardly" murder of Herve Gourdel would only strengthen France's resolve to pursue its air war against the Islamic State group in Iraq.

The 55-year-old was kidnapped on Sunday by Jund al-Khilifa, or "Soldiers of the Caliphate," while hiking in a national park that was once a magnet for tourists but later became a sanctuary for Islamists.

His beheading followed France's rejection of the group's 24-hour ultimatum to halt its air raids in Iraq -- part of a US-led campaign against IS.

Hollande, whose government was the first to join Washington in carrying out air strikes against the jihadists, pledged that France would stay the course.

"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."

US President Barack Obama voiced solidarity with France over the killing, which came after two American journalists and a British air worker were beheaded by IS in similar videotaped executions.

Chairing a special UN Security Council meeting, Obama looked at his French counterpart and said: "We stand with you and the French people as you grieve this terrible loss and as you stand up against terror in defence of liberty."

- 'Message with Blood' -

The video, entitled "A Message with Blood to the French Government", employs a similar style to those used in previous videos by IS showing the beheadings of three Western hostages.

It begins with a clip of Hollande at a press conference where he announced strikes against IS in Iraq.

The video then shows Gourdel on his knees with his hands behind his back in front of four armed militants, their faces covered.

The Frenchman briefly expresses his love for his family before one of the jihadists reads a speech in which he denounces the actions of the "French criminal crusaders" against Muslims in Algeria, Mali and Iraq.

The jihadist says the beheading is to "avenge the victims in Algeria... and support the caliphate" proclaimed by IS in Iraq and Syria.

The United States has built a coalition of more than 50 nations to fight IS, after the jihadists seized large parts of Syria and Iraq and committed widespread atrocities, including beheadings and crucifixions.

France has ruled out joining military operations in Syria, where a US-led coalition began strikes against IS on Tuesday.

Prime Minister Manuel Valls, in a speech Wednesday that kicked off a parliamentary session about France's engagement in Iraq, said it was not the cause of Gourdel's abduction.

"It's not our intervention that is exposing us to terrorism. The threat has been there for a long time. And that's why we are acting," Valls said.

The Algerian government called it "hateful" and expressed its "determination to continue the struggle against terrorism in all its forms and guarantee the protection and security of foreign nationals."

- Passionate mountaineer -

Gourdel had only arrived in Algeria on Saturday and was seized the following day while hiking in the heart of the Djurdjura National Park, whose dense forests, deep gorges and picturesque lakes were once a major attraction for tourists.

The mountains became a hideout for Islamists in the 1990s who later swore allegiance to Al-Qaeda, and security forces have been unable to dislodge them.

A passionate photographer and mountaineer, Gourdel liked going off the beaten track, though he was always careful, his friends said.

"I often bump into him in the mountains and he always goes to little-known areas of the massif, never on the major routes where there are people," said Michel Ingigliardi, his friend of 30 years in Saint-Martin-Vesubie, a village nestled deep in the French Alps.

"Going to far-away isolated countries is consistent with his personality."

The group that abducted him was formed recently after splintering from Al-Qaeda in the Islamic Maghreb (AQIM), which experts say has raked in some $120 million (93 million euros) in ransom payments in the past eight years.

Before the video was released, Gourdel's family expressed hope for his freedom and spoke of their anguish.

"We learned with great pain of the kidnapping of Herve Gourdel, our father, our partner, our son, our brother and our very dear friend," said a family statement sent to AFP Tuesday.

Family of British hostage pleads for release
London (AFP) Sept 23, 2014 - The wife of a British taxi driver held by Islamic State jihadists pleaded for his release on Tuesday, saying she had received a recording of him begging for his life.

Alan Henning, a 47-year-old Briton who volunteered to help drive an aid convoy to Syria for Muslim charity Aid4Syria, was kidnapped 10 months ago.

"An audio file of Alan pleading for his life has just been received by me," his wife Barbara said in a statement released through Britain's Foreign Office.

"He went to Syria to help his Muslim friends deliver much needed aid."

"We are at a loss why those leading Islamic State cannot open their hearts and minds to the facts surrounding Alan's imprisonment and why they continue to threaten his life."

It was the family's second appeal since Henning, a father of two teenage children, was threatened in a video that showed the brutal killing of British aid worker David Haines earlier this month.

Barbara Henning said that her attempts to communicate with the IS group had been ignored, and that she had learned that Henning had been cleared by an Islamic law court.

"I have been told that he has been to a Sharia Court and found innocent of being a spy and declared to be no threat," she said.

"I implore Islamic State to abide by the decisions of their own justice system. Please release Alan."

The appeal came after the release of a new video of another British hostage, freelance photojournalist John Cantlie, who first appeared last week in a video in which he announced he was being held captive by IS.

The new video is introduced as "Episode 1" in a series, and shows Cantlie criticising the actions of Western governments in a pre-prepared script.

On Tuesday the United States and Arab allies attacked jihadists within Syria in bomb and missile strikes, a turning point after years of reluctance from the West to intervene in Syria's civil war.

Following the strikes the brother-in-law of the kidnapped Henning said he feared the move could make it harder to find and rescue the hostage as militants fled attacks.

"They'll take him with them and no one will know where he is again," Colin Livesey told ITV News.