French Foreign Minister Laurent Fabius has said that France's involvement in the campaign against Islamist rebels in Mali will last "a matter of weeks".
On Sunday, French warplanes bombed the town of Gao in eastern Mali, extending their raids deep into rebel territory.
France's military began action against the militants in Mali on Friday. It has called a meeting of the UN Security Council for Monday.
Islamists have vowed attacks on French soil in revenge for the campaign.
Speaking to French media, Mr Fabius rejected any parallel with the protracted Western mission in Afghanistan.
"Later on, we can come as back-up, but we have no intention of staying forever," he said.
Mr Fabius said that had France not intervened, there was a risk that the Islamists could have advanced as far as the capital, Bamako, with "appalling consequences".
The French intervention had succeeded in stopping their advance towards the south, he added.
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 died.
Human Rights Watch believes 10 civilians, including three children, died in the town of Konna as Malian forces fought to recapture it.
The mayor of Gao, Sadou Arouna Diallo, who is now living in Bamako, thanked the French government for its intervention. He told the BBC: "The bombings are very well targeted... the residents are very satisfied."
A resident of Gao confirmed to the BBC that the strikes were outside of the centre and "extremely accurate".
"I cannot give you the precise figure about the casualties," he said. "But I can tell you there has been extensive damage and a huge loss of life. It's difficult to say who's in control in Gao now."
Islamist groups and secular Tuareg rebels took advantage of chaos following a military coup to seize northern Mali in April 2012.
But the Islamists soon took control of the region's major towns, sidelining the Tuaregs.
One Islamist group, Ansar Dine, began pushing further south last week, seizing 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 from countries in Ecowas, the West African regional bloc, had not been expected until the autumn.
However, Mr Fabius said that "terrorists" had taken advantage of this delay to attack, prompting Mali's interim president to ask for French intervention.
French 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.
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.
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.
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.
France has sent around 550 troops to the central town of Mopti and 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 now expected to arrive in Mali within days.
The UK has provided two C17 transport planes to aid the French effort.
Islamist groups in West Africa 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 France on Saturday.
On Monday, Abou Dardar, a spokesman for the al-Qaeda-linked Mujao, told AFP: "France has attacked Islam. We will strike at the heart of France."
He said the attacks would be "everywhere. In Bamako, in Africa and in Europe".