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French President Francois Hollande has strongly condemned the beheading in Algeria of tourist Herve Gourdel by a jihadist group linked to Islamic State (IS) militants.

 The president described 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 killed Mr Gourdel, 55, after its deadline for France to halt air strikes on IS in Iraq ran out.

Algeria said it would do everything possible to bring the killers to justice.

"Algeria will never ever bend to terrorism and justice will be done. Our commitment to fight this scourge will grow even stronger," said Foreign Minister Ramtane Lamamra.

'Never cede to terrorism'

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

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

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

"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.

Speaking on the sidelines of the assembly, the president said that Mr Gourdel - who was seized on Sunday - was dead because he was the representative of French people who "defend human dignity against barbarity".

"France will never cede to terrorism because it is our duty, and, more than that, because it is our honour.''

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

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 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.

Who are Jund al-Khilafa?

Previously part of al-Qaeda in the Islamic Maghreb (AQIM), which grew out of Algerian Islamist groups involved in 1990s civil war

Carried out numerous attacks in Kabylie region - in April, ambushed an army convoy, leaving 11 soldiers dead

Many residents have fled the region's forests and mountains in recent years because of insecurity

Group said to be led by Abdelmalek Gouri, known as Khaled Abou Slimane, 37

On 14 September, pledged allegiance to Islamic State

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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.

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.

Source: BBC