France has confirmed that an Algerian jihadist group linked to Islamic State (IS) militants has beheaded tourist Herve Gourdel, seized on Sunday.

Jund al-Khilafa killed Mr Gourdel, 55, after its deadline for France to halt air strikes on IS in Iraq ran out.

French President Francois Hollande condemned the killing as a "cruel and cowardly" act.

He said that French air strikes which began on IS targets in Iraq last week would continue.

Jund al-Khilafa posted a video of Mr Gourdel being killed which was entitled "Message of blood for the French government".

Police are guarding Herve Gourdel's home in Nice, south-eastern France.

Posters in support of Herve Gourdel were put up in the village of Saint-Martin-Vesubie, south-eastern France.

The Kabylie region is a rugged and mountainous area of Algeria

IS itself has beheaded three Western hostages since August: US journalists James Foley and Steven Sotloff, and British aid worker David Haines. Their deaths were all filmed and posted online.

The group has also threatened to kill Alan Henning, a taxi driver from the UK, who was seized while on an aid mission to Syria in December.

On Sunday, it warned it would target Americans and other Western citizens, "especially the spiteful and filthy French".

'Odious ultimatum'

Police have been guarding Mr Gourdel's home in the French city of Nice. He worked as a mountain guide in the Mercantour national park north of the city.

He had also been organising treks through the Atlas Mountains of Morocco for some 20 years, AFP news agency reports.

In the video posted by his killers, he is shown on his knees with his hands behind his back in front of four masked, armed militants.

He is allowed briefly to express his love for his family before one of the militants reads out a speech in which he denounces the actions of the "French criminal crusaders" against Muslims in Algeria, Mali and Iraq.

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

Jund al-Khilafa (Soldiers of the Caliphate) pledged allegiance to IS on 14 September.

Until then it had been known as part of al-Qaeda in the Islamic Maghreb (AQIM), which grew out of an Algerian militant group and is now active across North and parts of West Africa.

The group claimed Toulouse gunman Mohamed Merah, a French citizen of Algerian origin, as a member after he killed seven people in south-western France in March 2012, French radio reports.

The militants said that they were responding to the IS call to attack citizens involved in strikes on Iraq and would kill Mr Gourdel unless France ended its military operation.

On Tuesday, President Hollande said: "As grave as this situation is, we will not give into any blackmail, any pressure, any ultimatum no matter how odious, how despicable."

France's public position is that it does not negotiate with militant groups but there have been reports of French citizens being released in West Africa after ransoms have been paid.

Four Frenchmen kidnapped in Niger were freed in October 2013 amid reports of a 20m-euro (£16m; £25m) ransom being paid. The government in Paris denied that was the case.