The French have made much ground, but there are fears rebels may re-group in the mountains near Kidal
French warplanes have carried out air strikes in Mali's far north as they try to secure the final rebel stronghold of Kidal after a three-week offensive.
Thirty jets targeted Islamist militants' training and communication centres around Tessalit - a mountainous area near the Algerian border.
French President Francois Hollande has pledged to help rebuild Mali after the rebels who seized its north are beaten.
But there are fears the fighters could re-group in the mountains near Kidal.
It is believed that several French civilian hostages are being held by militants in the area, making the situation even more delicate.
Although French troops captured Kidal's airport on Wednesday, rebels from a Tuareg group who want their own homeland in northern Mali - the MNLA - still have control of the town itself.
Malian Interim President Dioncounda Traore has offered to hold talks with the MNLA in order to help secure Kidal.
It may be that this is achieved through diplomacy rather than through force, says the BBC's Thomas Fessy in Mali's capital, Bamako.
At the same time, French-led forces will begin chasing down Islamist militants who have retreated to desert or to mountainous hide-outs, adds our correspondent.
Reports have also emerged that a senior figure in the main militant Islamist movement - Ansar Dine - has been captured near the Algerian border by a rival separatist group.
Malian security sources quoted by AFP news agency named the man as Mohamed Moussa Ag Mouhamed, third in command of the group. The report cannot be verified.
Speaking in Bamako on Saturday, Mr Hollande pledged more French aid to its former colony and vowed to restore cultural sites damaged by the rebels.
Mr Hollande received a warm welcome on Saturday as he visited the northern desert city of Timbuktu, which was recaptured by French and Malian troops a week ago.
A total of 3,500 French troops are currently in Mali.
Nearly 2,000 army personnel from Chad and Niger are already helping consolidate the recent gains. A further 6,000 troops will be deployed as part of the UN-backed African-led International Support Mission to Mali (Afisma).
Despite the rapid progress of French forces in recapturing parts of the north, it may be premature to talk of mission accomplished, analysts say.
It is thought the mountainous areas around Kidal provide perfect hiding places for the militants.
On Saturday Mr Hollande said it would be wrong to assume the operation was over while Mr Traore said it would be difficult to completely rid the country of Islamists.