Jihadists linked to the Islamic State group beheaded a Frenchman abducted in Algeria in a video posted online Wednesday, after Paris rejected their demand to halt air strikes in Iraq.

President Francois Hollande condemned the "cruel and cowardly" murder of Herve Gourdel and said it would only strengthen France's resolve to pursue its air war against the Islamic State group.

Paris will not make any concessions to jihadists who have threatened to kill a French hostage in Algeria, President Francois Hollande said Tuesday.

"As grave as this situation is, we will not give into any blackmail, any pressure, any ultimatum no matter how odious, how despicable," he said, vowing to continued support for Iraqi authorities battling jihadists.

An Algerian militant group said it has kidnapped a Frenchman and threatened to execute him unless Paris halts air strikes on Islamic State jihadists in Iraq, in a YouTube video posted Monday.

Jund al-Khilifa, which has pledged allegiance to IS, said it carried out Sunday's kidnapping in a mountainous region of eastern Algeria where al-Qaida is active.

Algerian soldiers have killed a "terrorist chief" during an operation in the Kabylie region some 110 kilometers (70 miles) east of the capital, the defense ministry announced on Monday.

"As part of the anti-terrorist struggle and acting on information received, an army detachment on Sunday eliminated a terrorist chief responsible for several crimes in the region," the ministry's Internet site reported.

Algeria will impose more government control on training for the country's imams in a bid to fight Islamic extremism, its religious affairs minister said in comments published in local media on Wednesday.

The former French colony in North Africa has a difficult history with religious fundamentalism, having fought hardline Islamists during a bloody civil war in the 1990s that left some 200,000 people dead.

A suspected lieutenant of al-Qaida-linked Algerian jihadist commander Mokhtar Belmokhtar has been arrested in northern Mali, security sources said on Friday.

Rebel groups in the northeastern separatist stronghold of Kidal arrested Meherig Jafar before handing him over to the authorities via the French army, a source from the United Nations peacekeeping mission told Agence France-Presse.

Tunisian police and Islamists protesting against the arrest of a militant have clashed in the southern town of Douz, the interior ministry said on Friday.

Peace talks between the Malian government and armed rebels opened on Monday in the Algerian capital, the second round of negotiations since July aimed at clinching a lasting peace agreement.

The Bamako government and six rebel groups, mostly Tuareg but also including Arab organizations, are seeking to resolve a decades-old conflict that created a power vacuum in the desert north that was exploited by al-Qaida.

Malian government negotiators will sit down with separatist militias on Monday, hoping to end the conflicts that continue to rage in the country a year after it returned to democracy.

Riven by ethnic rivalries, a Tuareg rebellion and an Islamist insurgency in its vast desert north, the west African nation has struggled for stability and peace since a military coup in 2012.

Two Algerian diplomats kidnapped in Mali in April 2012 by the Movement for Oneness and Jihad in West Africa (MUJAO) were freed on Saturday, the Algerian foreign ministry announced.

A third diplomat, consul Boualem Sayes, had died in captivity "from a chronic illness", the ministry said.