President Francois Hollande says more French troops are to be deployed in Mali to support the 750 in the country countering an Islamist insurgency.
Mr Hollande said new air strikes overnight had “achieved their goal”. One target was the town of Diabaly, which rebels entered on Monday.
West African military chiefs are meeting in Mali to discuss how an alliance with the French will work.
France began its intervention on Friday to halt the Islamists’ advance south.
Late on Monday, the UN Security Council unanimously backed the intervention.
Mr Hollande, on a visit to the French regional military base known as Peace Camp in Abu Dhabi, said: “For now, we have 750 men and the number will increase. New strikes overnight achieved their goal.”
France to boost troops in Mali
He said that assembling an African military force to work with the French troops could take a “good week”.
Mr Hollande told RFI radio: “We are confident about the speed with which we will be able to stop the aggressors, the enemy, these terrorists.”
The French contingent is expected to rise to 2,500 in the coming weeks.
Witnesses in Diabaly, 400km (250 miles) north-east of Mali’s capital, Bamako, said there had been major air strikes overnight to try to dislodge Islamists who had taken the town from Malian forces on Monday.
However, Mr Hollande said the Islamists had not captured it, but were merely hiding there “to protect themselves”, adding: “They will be chased out.”
One visitor, Ibrahim Toure, told the Associated Press (AP) news agency: “They bombed the town all night long. I am hiding inside a house. It only stopped at around 06:00.”France to boost troops in Mali
One Malian security source told Agence France-Presse (AFP) news agency that “at least five Islamists were killed and many injured”.
Some 30 French tanks and armoured troop transport vehicles also crossed into Mali from Ivory Coast on Monday with a helicopter escort, witnesses said.
The BBC’s Mark Doyle in Bamako says the French want ground reinforcements from West African allies as soon as possible.
He says the meeting of regional military commanders in the Malian capital will discuss equipment needs and how a military alliance with France will work in practice.
Ivory Coast army chief Gen Soumaila Bakayoko said: “We are here today to speak essentially about the engagement alongside our Malian brothers in arms, to liberate the north of Mali.”
Nigeria is set to lead the regional force, supplying 600 troops.
The African force will be deployed under UN Security Council resolution 2085, which was passed in December and allows for a 3,000-strong mission.
French Foreign Minister Laurent Fabius says there will be a donor meeting towards the end of January to discuss the funding of the anti-Islamist intervention.
He also denied the French intervention would boost al-Qaeda recruitment.
“It’s not encouraging terrorism to combat terrorism,” he said.
French warplanes have carried out a series of air strikes since the intervention began on Friday.
Islamists are reported to have withdrawn from the major towns of Timbuktu and Gao.
One spokesman for the Ansar Dine militant group, Senda Ould Boumama, said the withdrawal was a “tactical retreat” to reduce civilian casualties.
One resident of Timbuktu told AFP: “The mujahideen have left. They are really scared.”
However, one spokesman for the Islamist group, the Movement for Oneness and Jihad in West Africa, told AP: “I would advise France not to sing their victory song too quickly. They managed to leave Afghanistan. They will never leave Mali.”
On Monday, the UN Security Council convened in New York for an emergency meeting at France’s request.
France’s UN ambassador Gerard Araud said his country had the “understanding and support” of the 14 other Security Council members.
A meeting of EU foreign ministers in Brussels on Thursday will discuss EU involvement.
At least 11 Malian soldiers and a French helicopter pilot have died in Mali since Friday’s intervention. More than 100 militants are reported to have been killed.
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.
The UN says some 144,500 Malian refugees have been registered in neighbouring countries since April 2012.
It also says that 30,000 people have been displaced as a direct result of conflict this month.