France's military aim in Mali is its "total reconquest", French Defence Minister Jean-Yves Le Drian has said.
"We will not leave any pockets" of resistance, he told French television.
France has sent in 2,000 troops to help Malian forces fight Islamist militants who now control the northern half of the country.
Mr Le Drian said the former Islamist stronghold of Diabaly had not yet been retaken, even though the militants withdrew from the town two days ago.
However, he added that "everything points to a favourable evolution of the situation in Diabaly in the coming hours".
Mr Le Drian also said during his interview that seven French citizens who had been taken hostage in Niger and Mali in recent years "are alive", and there had been "contacts with hostage-takers".
There had been concerns for their fate following France's decision to send troops into Mali earlier this month.
French troops have been pushing northwards and are now in the town of Niono, 50km (30 miles) south of Diabaly.
Last week French forces carried out air strikes on Diabaly, which had fallen to the Islamists on 14 January.
Diabaly's mayor told the BBC that Malian and French forces had been patrolling the outskirts of the town, which is believed to be the base for the largest concentration of Islamists in central Mali.
The BBC's Mark Doyle, in Niono, says military patrols are being sent from there into Diabaly.
Officials say the Islamists left Diabaly on Friday. However, the Malian military suspects the fighters are hiding in a nearby forest, our correspondent says.
"The situation in the vicinity of Diabaly is confused for the moment," a French colonel who gave his name only as Frederic told our correspondent.
A senior Malian military figure cautioned that parts of Diabaly's population were sympathetic to the Islamists, and this made their task difficult.
Officials say Mali's army has also retaken the town of Konna, whose capture by rebels triggered the French intervention.
Jean-Yves Le Drian's comments to French television echo a similar sentiment by President Francois Hollande who said French troops would remain in the region for as long as is necessary "to defeat terrorism".
But French Foreign Minister Laurent Fabius on Saturday stated that West African countries must "pick up the baton" in the offensive to drive out the Islamists.
Ivory Coast President Alassane Ouattara also called for more support for Mali, at a summit of West African leaders in Abidjan attended by Mr Fabius.
The French foreign minister has said both Russia and Canada had offered logistical support.
Islamist militants in Algeria who seized a gas facility in the Sahara desert, killing foreign hostages, claimed the attack was in retaliation for the French intervention in Mali, though many analysts doubt this.