Jean-Yves Le Drian, the French defence minister, said ground troops had not yet taken another target, Diabaly, but expected positive news "in the coming hours".
He added: "French forces, and notably air forces, are striking terrorist strongholds. That's the case in the region of Gao, it's the case in the Timbuktu region. It will continue."
Yesterday French troops in armoured vehicles advanced towards Diabaly, which was abandoned by Islamist rebels after days of airstrikes.
Television showed the wreckage of the Islamists' pick-up trucks, some with heavy machine guns mounted on them, lying charred and twisted in the village.
Commanders of French and Malian forces have set up their operations centre in the nearby town of Niono, 190 miles northeast of the capital Bamako.
"Our principal concern is that a section of the population may have joined the jihadists," said Colonel Seydou Sogoba, head of the Malian military operation. "The war against the Islamists is not an easy one. They come in and mix with the local population."
Some Islamist fighters had shaved off their beards and swapped their robes for jeans to blend in with locals, he said.
France has deployed 2000 troops and its planes have pounded rebel columns and bases for 10 days, effectively halting an Islamist advance on the capital.
French intervention was aimed at stopping a coalition of Muslim militants using Mali's north as a springboard for attacks in Africa and on the West.
The Islamist alliance, grouping al Qaeda's North African wing AQIM and home-grown Malian militant groups, has imposed harsh sharia law in northern Mali, including amputations and the destruction of moderate Sufi Muslim shrines.
In Paris, Foreign Minister Laurent Fabius brushed off the idea that France risked getting embroiled in a guerrilla war.
Islamist fighters have pledged to turn Mali into a new Afghanistan, but he said: "In Afghanistan, there was no democratic regime. Here, there's a democratic regime even if it needs to be perfected."
The stakes in Mali rose dramatically this week when Islamist gunmen cited France's intervention as the reason behind the hostage-taking at an Algerian gas plant. More than 50 people including 23 hostages died when Algerian forces retook the plant.
The conflict in Mali and the hostage crisis in Algeria have raised concerns about the radicalisation of the broader Sahel region, which is awash with weapons from the Libyan civil war.
At a meeting with heads of state from West African regional group ECOWAS in Ivory Coast on Saturday, Mr Fabius appealed for international funding for a UN-backed African mission to oust the Islamists from the region.
Military experts say France and its African allies must deploy troops fast to capitalise on gains and stop insurgents regrouping, but African forces are hampered by a lack of transport and supplies. Nigeria, Niger and Togo have put in a few hundred troops and 50 Senegalese soldiers left for Bamako yesterday.
Human Rights Watch warned on Saturday it had received reports of serious abuses, including killings, being committed by Malian security forces against civilians in Niono.