His beheading, which was posted online in a video, came after France rejected the kidnappers' 24-hour ultimatum to halt anti-IS air raids in Iraq.
Voicing solidarity with France, US President Barack Obama 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."
France was the first country to join Washington in carrying out an aerial campaign against IS jihadists in Iraq.
President Francois Hollande pledged that his country would stay the course in the fight against the jihadists.
"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 European Union said the killing was "a further demonstration of the determination of groups affiliated to (the IS group) to pursue and extend their terror strategy".
No effort must be spared to hold the perpetrators accountable for the "barbaric murder", it added.
The Algerian government, which had mobilised troops to scour the mountains for Gourdel, condemned the "hateful" murder.
It also voiced its "determination to continue the struggle against terrorism in all its forms and guarantee the protection and security of foreign nationals present on its territory."
- 'National mourning' -
Emotions ran high in Gourdel's home town of Nice after news of the murder broke, with flags in the city flying at half mast.
The deputy mayor of the French riviera resort, Christian Estrosi, visibly moved, told reporters that the country had been plunged into "national mourning" after he met with Gourdel's relatives late on Wednesday.
"It's a terrible shock" for the parents, he said, adding that the family had reacted to Gourdel's death "with dignity, anger and an unspeakable pain".
Nice resident Odile, who did not know Gourdel personally but lives near his building, said she was "disturbed" by his death. "I'm very surprised to see this horror that we are finding ourselves in," she said.
Further north in Saint-Martin-Vesubie, where Gourdel worked as a guide in the Mercantour national park, mayor Henri Guige said he was "shocked". "For me, this is a war in which they are attacking civilians, the innocent," he told AFP.
A passionate photographer and mountaineer, Gourdel liked going off the beaten track, though he was always careful, his friends had said.
Close friend Laurent Geny described him as someone who is "profoundly good, very humane and who loves the Maghreb culture".
"No one deserves to go through that. But him even less because he knew the Maghreb well, he had strong links with the Maghreb," he added.
Gourdel had for years trained mountain guides in Morocco.
Prime Minister Manuel Valls turned to Twitter to express his outrage. "The support of the whole nation goes to Herve Gourdel's family. France will never give in," he wrote.
Gourdel's murder comes after three Western hostages -- two US journalists and a British aid worker -- have been beheaded by IS since August.
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Voicing solidarity with France, US President Barack Obama 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."
France was the first country to join Washington in carrying out an aerial campaign against IS jihadists in Iraq.
President Francois Hollande pledged that his country would stay the course in the fight against the jihadists.
"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 European Union said the killing was "a further demonstration of the determination of groups affiliated to (the IS group) to pursue and extend their terror strategy".
No effort must be spared to hold the perpetrators accountable for the "barbaric murder", it added.
The Algerian government, which had mobilised troops to scour the mountains for Gourdel, condemned the "hateful" murder.
It also voiced its "determination to continue the struggle against terrorism in all its forms and guarantee the protection and security of foreign nationals present on its territory."
- 'National mourning' -
Emotions ran high in Gourdel's home town of Nice after news of the murder broke, with flags in the city flying at half mast.
The deputy mayor of the French riviera resort, Christian Estrosi, visibly moved, told reporters that the country had been plunged into "national mourning" after he met with Gourdel's relatives late on Wednesday.
"It's a terrible shock" for the parents, he said, adding that the family had reacted to Gourdel's death "with dignity, anger and an unspeakable pain".
Nice resident Odile, who did not know Gourdel personally but lives near his building, said she was "disturbed" by his death. "I'm very surprised to see this horror that we are finding ourselves in," she said.
Further north in Saint-Martin-Vesubie, where Gourdel worked as a guide in the Mercantour national park, mayor Henri Guige said he was "shocked". "For me, this is a war in which they are attacking civilians, the innocent," he told AFP.
A passionate photographer and mountaineer, Gourdel liked going off the beaten track, though he was always careful, his friends had said.
Close friend Laurent Geny described him as someone who is "profoundly good, very humane and who loves the Maghreb culture".
"No one deserves to go through that. But him even less because he knew the Maghreb well, he had strong links with the Maghreb," he added.
Gourdel had for years trained mountain guides in Morocco.
Prime Minister Manuel Valls turned to Twitter to express his outrage. "The support of the whole nation goes to Herve Gourdel's family. France will never give in," he wrote.
Gourdel's murder comes after three Western hostages -- two US journalists and a British aid worker -- have been beheaded by IS since August.
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