French warplanes have bombed the town of Gao in eastern Mali, extending their attacks deep into rebel-held territory.
France's military has been in action against Islamist militants in Mali since Friday, helping government forces recapture the central town of Konna.
A resident in Gao told AFP news agency all Islamist bases in the town had been destroyed and the militants had fled.
French Foreign Minister Laurent Fabius said the Islamist advance in Mali had been brought to a halt.
"Stopping the terrorists, that's done," he told RTL radio. Had France not intervened, there was a risk that the Islamists could have advanced as far as the capital, Bamako, he said.
Islamist groups and secular Tuareg rebels seized northern Mali in April 2012.
But the Islamists soon took control of the region's major towns and one group, Ansar Dine, began pushing further south last week, seizing the strategically important town of Konna.
The town has since been recaptured by Malian troops with French aerial support.
France's decision to intervene in its former colony took many by surprise. A UN-backed international force had not been expected in the west African state until the autumn.
France has called a meeting of the UN Security Council to discuss its action on Monday.
The foreign minister made it clear that France was now targeting Islamist bases in the north and said Algeria, which shares a long border with Mali, had given permission for its air space to be used for bombing raids "without limit".
For months, Gao has been in the hands of the Movement for Oneness and Jihad in West Africa (Mujao), which along with Ansar Dine has sought to enforce an extreme interpretation of Islamic law in northern Mali.
The town is around 500km (310 miles) north-east of a de facto line dividing the rebel-held north of Mali from the government-run south.
Defence Minister Jean-Yves Le Drian said four Rafale fighter jets, flying from their base in France, had attacked and destroyed rebel training camps and logistics depots in Gao, which acted as back-up bases for terrorist groups.
The air attacks were continuing as part of an offensive to drive back Islamist militants who still controlled large swathes of northern Mali, he said earlier.
"There were [air strikes] last night, there are now and there will be today and tomorrow," the minister said.
BBC Africa correspondent Andrew Harding says it seems clear that French air power is now preparing the ground for a much bigger offensive against the Islamists.
A spokesman for Ansar Dine Islamist group was quoted as saying that the French attacks had focused on three areas: Konna, Douentza and Lere.
But later reports said French bombers had also targeted the northern town of Kidal, described as a headquarters for Ansar Dine and its leader Iyad Ag Ghaly.
Fearing further French air raids, the group's fighters have moved out of the historic town of Timbuktu, Sahara Media report from neighbouring Mauritania.
'Guys with guns'
An unnamed Elysee Palace official quoted by AFP said on Sunday that French armed forces had been surprised by the fighting quality and the equipment of the militants they were up against.
"At the start, we thought they would be just a load of guys with guns driving about in their pick-ups, but the reality is that they are well-trained, well-equipped, and well-armed," the official said.
"From Libya they have got hold of a lot of up-to-date, sophisticated equipment which is much more robust and effective than we could have imagined."
France has sent around 550 troops to the central town of Mopti and the capital, Bamako. They are set to be joined by troops from the neighbouring African states of Niger, Burkina Faso, Nigeria and Togo, some of which are expected to arrive in Mali within days.
In December, the UN Security Council backed sending a 3,300-strong force from the Ecowas West African regional bloc to recapture rebel-held areas of Mali but their deployment was not expected for some months.
The UK has provided two C17 transport planes to aid the French effort and Mr Fabius said practical support was also coming from the US, Denmark and other European countries.
A Malian army officer said on Saturday he believed more than 100 militants had been killed.
Since the start of the French intervention on Friday, at least 11 Malian soldiers and a French helicopter pilot have also died.
Human Rights Watch believes 10 civilians, including three children, died in Konna as Malian forces fought to recapture the town.
Medical aid agency MSF said many civilians had fled the Mopti area and some places had become "almost ghost towns". Hundreds of people had already fled over the border into Mauritania, it said.
Islamist groups are still holding several French hostages and have threatened reprisals against them and other French targets.
This prompted the French government to step up security across the country on Saturday.