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France says the goal of its military action in Mali is to retake control of the entire country from Islamist militants who have seized the north.
The comment came as French troops consolidated gains in Mali's Islamist-held north as part of their advance on Al Qaeda-linked militants.
According to News.com.au, they are closing in on the mountainous region of Kidal, 930 miles from Bamako, near the border with Algeria.
The BBC cited Le Drian as saying that the town of Diabaly, formerly a militant stronghold, had not yet been retaken, however, "everything points to a favourable evolution of the situation in Diabaly in the coming hours".
France has sent in 2,000 troops to help African forces fight Islamist militants who had taken control the country's vast desert north since March last year.
The militants joined anti-government Tuareg separatists in but the two groups had since had a falling out, and the Islamists have since gained the upper hand.
Meanwhile, according to Le Drian, seven French citizens had been taken hostage by Islamist militants in Niger and Mali in recent years and were still alive.
French Foreign Minister Laurent Fabius said over the weekend that West African troops needed "to take the lead" in driving out Islamists, The New York Times reported.
However, Le Drian has since said on France 5 television:
"The goal is the total reconquest of Mali. We will not leave any pockets."
According to the BBC, his comments echo a similar sentiment by President Francois Hollande, who had said French troops would remain in the region long enough "to defeat terrorism".