French soldiers patrol in northern Mali on March 1. (Ghislain Mariette/AP)

As the French army and its desert-savvy Chadian allies pursue Islamist guerrillas into remote hideouts in northeastern Mali, concern has arisen here that 15 French hostages held by Muslim extremists could fall victim to President Francois Hollande’s apparent determination to destroy Africa’s jihadi network once and for all.

The fate of French hostages has from the beginning been one of the major risks inherent in the large-scale military intervention in Mali launched Jan. 11 after an unexpectedly swift decision by Hollande to help repel an Islamist attack southward toward the capital, Bamako.

Hollande has maintained that wiping out the guerrilla groups linked to al-Qaeda in the Islamic Maghreb (AQIM) is the only effective way to resolve the often-repeated drama of French citizens being taken captive in northwestern Africa. But as his troops close in on the hostage-takers’ last Malian refuge, the rock-strewn Adrar des Ifoghas mountains, families of the hostages have voiced fears that their loved ones could be executed in an act of desperation by trapped Islamist fighters.

Families of four of the hostages issued a statement Monday calling on Hollande to suspend attacks temporarily to allow time for negotiations with the Islamist guerrillas, saying “the intensity of clashes can endanger our loved ones’ lives, and we believe each encounter could be fatal to them.” The Islamist groups took their captives in part as collateral for such negotiations, they reasoned, and so Hollande should give talks a chance before the irreparable happens.

“After the military operations, we need a pause, a strategy that, instead of being a strategy of force, is a strategy of political opening and dialogue,” said Pierre Robert, grandfather of Pierre Legrand, who has been held in the embattled Sahel region since September 2010.

There was no direct response from Hollande, but French officials made it clear that their combat operations would continue despite the families’ fears.

“We are going to finish the job,” said a senior official who spoke on the condition of anonymity to discuss sensitive information.

Defense Minister Jean-Yves Le Drian said in a television appearance Tuesday that he and Hollande understand the anguish about the hostages and that, from the information available to the French government, “we have every reason to believe they are alive.”

Le Drian described clashes underway in the northeastern Mali mountains, which include close-range combat with assault rifles, as “some of the most violent” since the operation began. Two French soldiers have been killed there in the past 10 days, bringing to three the number of French service members killed during the intervention.

French commentators speculated that at least some of the hostages are held in the Adrar des Ifoghas range because the region is where AQIM and related guerrilla groups had their headquarters and stored their arsenals of assault rifles, explosives and gasoline. But Adm. Edouard Guillaud, the French military’s chief of staff, said in a radio interview Monday that French authorities have no solid information on where the hostages are held and added that they could have been dispersed to other hideouts.

Guillaud said reports from the Chadian government that Chadian soldiers had killed Abdelhamid Abu Zeid, the region’s preeminent AQIM leader, were probably true. But he added that France has yet to identify the body and so could not be sure.

A Mauritanian Internet site, Sahara Medias, quoted Islamist leaders as confirming Abu Zeid’s death, which they said occurred during a French bombing raid against one of his mountain redoubts. But the sources denied Chadian claims that the attacking French and Chadians had also killed another prominent AQIM leader, Mokhtar Belmokhtar, a one-eyed guerrilla chief who led a mass hostage-taking Jan. 16 at a remote Algerian gas-producing facility.

The overall AQIM leader, Abdelmalik Droukdel, has remained silent in his hideout in northern Algeria throughout the French offensive.

Despite Hollande’s silence, Guillaud and other French officials expressed satisfaction at news that Abu Zeid and other AQIM leaders have probably been killed. Abu Zeid was the most active hostage-taker among the several groups of al-Qaeda-linked Islamists who had made northern Mali a sanctuary after Tuareg independence militias drove the Malian army out of the region in March.

“We are in the process of breaking the back of AQIM, and that was the goal as it was fixed by the president of the republic,” Guillaud said.

But for the families of hostages, the announced deaths of Abu Zeid and Belmokhtar raised the specter of desperate and leaderless extremists unable to decide what to do with their prisoners, and perhaps killing them as a way to ease their escape to neighboring deserts. “Today we consider that military operations, of force, will not be able to save the hostages,” Robert said in a statement.

Of the 15 known French hostages, seven are believed to be held by AQIM and related Islamist groups in Mali. An eighth was captured in Nigeria, but his location has not been revealed. Seven others — four children, their parents and their uncle — were captured last month in northern Cameroon and transferred to Nigeria in the custody of Boko Haram, a Nigeria-based Islamist group with extremist goals similar to those of AQIM.