The Algerian army said on Tuesday it had killed the head of a militant group that beheaded a French tourist after it had pledged allegiance to the Islamic State group.

The body of Abdelmalek Gouri, who claimed responsibility for the beheading of Frenchman Herve Gourdel in September, was identified after an operation in the town of Isser "that allowed us to eliminate three terrorists", the army said.

An operation lasting three months had seen 3,000 Algerian troops mobilised to catch Gourdel's killers.

The confirmation of Gouri's death came after the Nahar private television network said soldiers had killed him and two other militants late on Monday in Isser, about 60 kilometres (37 miles) east of Algiers.

Jund al-Khilafa, or "Soldiers of the Caliphate", beheaded Gourdel on September 24 in a gruesome video posted online after France rejected the group's demand to halt anti-IS air strikes in Iraq.

On Saturday, the army said it killed three other Islamist gunmen in a mountainous area near Sidi Daoud, and that one of them was a "dangerous criminal" wanted since 1995.

Soldiers also seized a large quantity of guns, ammunition and explosives during the operation.

On December 11, Justice Minister Tayeb Louh announced that soldiers had killed two Jund al-Khilafa members implicated in Gourdel's murder.

An Algerian court has launched legal proceedings against 15 people, including Gouri, suspected of participating in the beheading.

Gourdel, a 55-year-old mountain guide, was kidnapped in September while hiking in a national park that was once a draw for tourists but became a sanctuary for Islamists.

- Father identifies body -

He was later decapitated by Jund al-Khilafa, which was formed at the end of August after splintering from Al-Qaeda in the Islamic Maghreb and pledging allegiance to IS.

His killing followed calls by IS for Muslims to kill Westerners whose nations have joined a campaign to battle the jihadists in Iraq and Syria.

The defence ministry said in a statement it had received information that led to forces pursuing "a dangerous terrorist group travelling in a vehicle", before killing Gouri and two others.

A source familiar with the operation told AFP that the bodies of three suspected militants were taken to a local hospital, where Gouri's death was confirmed by his father early on Tuesday.

Violence involving Islamists has fallen considerably since the 1990s civil war, but groups linked to AQIM continue to launch attacks in the northeast, mostly on security forces.

Gouri, alias Khaled Abou Souleimane, was the former right-hand man of AQIM leader Abdelmalek Droukdel, and is suspected of helping to organise suicide attacks on the government palace and against a UN contingent in Algiers in 2007.

He is also thought to have masterminded an April attack that killed 11 soldiers in Iboudrarene, the same region where Gourdel was kidnapped.

The town of Isser in the Kabylie area is home to a large officer training school that was targeted in a 2008 suicide attack that killed dozens.

Gourdel's body has yet to be found, despite a widespread search by the army which has already found a Jund al-Khilafa hideout and identified the location where a video was filmed in August showing the group pledge fealty to IS.

Another two "dangerous terrorists" were killed on Tuesday in Akerrou, 120 kilometres southeast of Algiers, the army said.