Algerian militants have beheaded French tourist Herve Gourdel, who was kidnapped by gunmen on Sunday in what the group said was a response to France's action against Islamic State militants in Iraq.
In a video released by his captors, Gourdel, a 55-year-old from Nice, is seen kneeling with his arms tied behind his back before four masked militants who read out a statement in Arabic criticising France's intervention.
They then pushed him on his side and held him down. The video does not show the beheading, but a militant later holds the head up to the camera.
"This is why the Caliphate Soldiers in Algeria have decided to punish France, by executing this man, and to defend our beloved Islamic State," one of the militants says in the statement he read out.
France's President Francois Hollande confirmed the death of Gourdel, and vowed that French military operations against Islamic State would continue.
"Our compatriot has been killed cruelly and in a cowardly way by a terrorist group. Herve Gourdel was assassinated because he was French," Hollande, visibly shaken by the events, said at the United Nations. "My determination is total, and this aggression only strengthens it. France will continue to fight terrorists everywhere. The operations against Islamic State will continue."
The Caliphate Soldiers, a splinter group linked to Islamic State militants in Iraq and Syria, had on Monday published a video claiming responsibility for the abduction and showed the man identifying himself as Gourdel.
The kidnapping had come after Islamic State spokesman Abu Muhammad al-Adnani urged the group's followers to attack citizens of the United States, France and other countries that joined the coalition to destroy the radical group.
Just before the militants gave their statement in the video, the Frenchman told his family that he loved them.
There was no immediate comment from Gourdel's relatives, but a friend, Eric Grinda, told France's i-Tele television: "They want to fan the flames of hatred and to make us want to respond. They only are able to do one thing, assassinate a man on his knees with his hands tied ... My sadness is immense."
France launched its first air strikes targeting Islamic State targets in Iraq on Friday. It has said all must be done to rid the region of the group.
France raised the threat level at 30 of its embassies across the Middle East and Africa on Monday.
Deepening Islamist rivalries
Western diplomats and intelligence sources say they believe there are fewer than 10 Western hostages still held by Islamic State. The group has recently beheaded two Americans, James Foley and Steven Sotloff, and one Briton, David Haines, and threatened to kill another Briton, Alan Henning.
The Frenchman's kidnapping was one of the first abductions of a foreigner by militants in Algeria since the North African country ended its decade-long war with Islamist fighters in the 1990s.
There have, however, been many attacks in the Maghreb region carried out by armed Islamists. In January 2013, al Qaeda-linked militants took more than 800 people hostage at a gas facility near In Amenas, Algeria. Algerian special forces raided the site, but 40 workers were killed, all but one of them foreigners, along with 29 militants.
Gourdel, a French nature guide and photographer, was taken hostage when militants stopped his vehicle in the remote mountains east of Algiers where he planned a hiking trip, according to Algeria's interior ministry.
Algerian troops had launched a search for Gourdel in the mountains in an area known as the "Triangle of Death" during the bloody days of Algeria's 1990s war with Islamists. Though attacks from Islamists are rarer, al Qaeda in the Islamic Maghreb and other groups are still active.
The Caliphate Soldiers group earlier this month announced it had broken with al Qaeda in the Islamic Maghreb, known as AQIM, to back Islamic State, in another illustration of deepening rivalries between Islamic State and al Qaeda's core leadership.
AQIM central region commander Khaled Abu Suleimane, who claimed leadership of the Caliphate Soldiers, is a hardliner who has consistently refused peace agreements with the government and traces his militant roots back to the 1990s war.
In that war, 200,000 were killed, as militants fought a bloody campaign - cutting throats, massacring villages and kidnapping civilians - to overthrow the government and install an Islamic state in Algeria.