France's prime minister has insisted his country will not stop fighting Islamic State militants despite demands by kidnappers holding a French hostage.
The 55-year-old man was abducted in Algeria on Monday by a splinter group from al-Qaida's North African branch.
The Jund al-Khilafah, or Soldiers of the Caliphate, said it would kill the man - identified as mountain guide Herve Gourdel - unless France halts its airstrikes in Iraq within 24 hours.
French PM Manuel Valls said on Europe 1 radio that French authorities are "doing everything" to try to free the hostage, but will not negotiate with his captors.
He said: "If we cede, if we retreat one inch, that would hand victory to the militants."
On Friday, French forces joined the US in carrying out airstrikes against extremists who have over-run large areas of Syria and Iraq.
Algerian police and soldiers are continuing to search the Djura Djura mountains for Mr Gourdel.
In a video posted on Monday, the group calling itself the Jund al-Khilafah said it would kill him in 24 hours unless France ended its participation in airstrikes against the Islamic State group in Iraq.
An Algerian security official said the new group had split away from al-Qaida's North Africa branch just two weeks ago and declared allegiance to the Islamic State group in Syria and Iraq - a rival of al-Qaida.
The new Algerian group is led by 36-year-old Abdelmalek Gouri, also known as Khaled Abu Slimane, a veteran al-Qaida commander from the central region behind a series of bloody attacks on Algerian soldiers, said the official.
Mr Gourdel, a mountaineering guide from Nice, was taken on Sunday night while driving through the Djura Djura mountains in Algeria's rugged Kabylie region, which remains one of the last active areas of operation for al-Qaida in Algeria.
He was taken with four Algerian companions who were released.
At least 14 soldiers were killed in April close to where Mr Gourdel was kidnapped when they were ambushed by militants in an operation led by Mr Gouri, according to the official.
Residents told reporters that security has been deteriorating in the area for the last few days. Majid Benhamich, a local guard from the village of Akbil, said he was constantly being called up to help the army in its operations.
"There are frequent sightings of terrorists in the mountains and I hear there are some of foreign nationalities," he said, describing the area as still dangerous.
Laifa Bessadi, a resident of Ait Allaoua village just six miles from where Mr Gourdel was kidnapped, said the roads are filled with military trucks and there are helicopters in the sky. Everyone in his village has been ordered to stay at home.
"Last night, we heard gunshots in the night and this morning we saw helicopters firing, but we don't know what at," he said.
Algeria has been fighting Islamic extremists since the 1990s and in recent years they had been largely confined to a few mountainous areas, such as the Kabylie region, where they have concentrated on attacking soldiers and police while leaving civilians alone.
While the al-Qaida's branch in the Sahara has made millions off kidnapping foreign hostages, it has rarely killed them as the Islamic State group has now done with the two Americans and one Briton it held.
Djallil Lounnas, an expert on Islamic movements in North Africa, said the emergence of a group claiming loyalty to the Islamic State, a rival of al-Qaida, suggests that Abdelmalek Droukdel, the leader of the North African branch, is losing control of his men.
He said more attacks are to be expected as the new group tries to make a name for itself.
The US embassy in Algiers has renewed its travel warning for Algeria, urging Americans travelling there to "exercise vigilance" in their movements.