A French tourist has been kidnapped in Algeria by a militant group linked to Islamic State (IS), French Foreign Minister Laurent Fabius has confirmed.
Herve Gourdel, 55, was seized on Sunday in the unsettled north-east Kabylie area.
Algerian militant group Jund al-Khilafa threatened to kill him if France did not halt air strikes on Iraq.
Mr Fabius said an online video that showed Mr Gourdel flanked by armed men was authentic.
He said France would do everything it could to liberate Mr Gourdel, but that the situation was "extremely critical."
Islamic State militants warned on Sunday they would target Americans and other Western citizens, "especially the spiteful and filthy French", after French jets joined the US in carrying out strikes in Iraq on IS targets.
France on Monday raised the threat level for 30 of its embassies throughout the Middle East and Africa in response to what Interior Minister Bernard Cazeneuve called "yet another demonstration of the barbarism of these terrorists".
IS jihadists have seized large swathes of territory in eastern Syria and across northern and western Iraq, forcing tens of thousands of people to flee their homes this year.
French Prime Minister Manuel Valls said there would be "no discussion, no negotiation" with the kidnappers. "If you give in, if you go back one inch... you give [terrorism] this victory," he told French radio while on a visit to Germany on Tuesday.
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 fled the region's forests and mountains in recent years due to insecurity
- Group said to be led by Abdelmalek Gouri, known as Khaled Abou Slimane, 37
- 14 September, pledged allegiance to Islamic State
France's foreign ministry said in a statement: "We confirm the authenticity of the video showing images of French hostage Herve Gourdel, kidnapped in Algeria in the region of Tizi Ozou on Sunday."
"The threats made by this terrorist group show once again the extreme cruelty of [Islamic State] and those who say they are affiliated to it."
Speaking in New York, where he is attending the UN General Assembly, Mr Fabius told reporters: "We will do everything we can to liberate hostages... but a terrorist group cannot change France's position."
In the video, Mr Gourdel, flanked by two masked men, identifies himself as a 55-year-old from Nice, southern France.
Apparently speaking under duress, he said: "This armed group is asking me to ask you [French President Francois Hollande] to not intervene in Iraq."
French media say he is an experienced mountain guide and photographer with a taste for exploring, who set up a hiking centre in the Mercantour national park north of Nice.
The Algerian interior ministry said he and two Algerian companions had been driving through mountains near the village of Ait Ouabane, when they were stopped by armed men.
The gunmen let the Algerians go but seized the Frenchman.
Algerian group 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 murdered seven people in south-western France in March 2012, French radio reported.
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.
'Everything being done'
President Francois Hollande's office said he had spoken to Algerian Prime Minister Abdelmalek Sellal by phone and that there was "total co-operation" to try to find Mr Gourdel.
"Authorities are mobilised and no hypothesis is being discarded," the French government added.
Kabylie is a rugged, mountainous region which has seen several kidnappings of Algerian businessmen for extortion. AQIM has carried out deadly attacks in Kabylie this year.
Most of those who were abducted were later freed by security forces.