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, visiting the United Arab Emirates, said new air strikes overnight had “achieved their goal”.
West African military chiefs will meet in Mali on Tuesday to discuss how an alliance with the French will work.
France began its intervention on Friday with the aim of halting the Islamists’ advance south towards the capital.
Late on Monday, the UN Security Council unanimously backed the intervention.
‘Really scared’
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.”
He said that assembling an African military force to work with the French troops could take a “good week”.
The French contingent is expected to rise to 2,500 in the coming weeks.
Some 30 French tanks and armoured troop transport vehicles 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 regional military commanders are meeting in the Malian capital on Tuesday to discuss equipment needs and how a military alliance with France would work in practice.
Nigeria is set to lead the regional force, supplying 600 troops. Benin, Burkina Faso, Ghana, Niger, Senegal and Togo have also pledged soldiers. Britain has deployed troop transporters.
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.
‘Chase them away’
French war planes 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Islamists are reported to have withdrawn from the major towns of Timbuktu and Gao.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 Agence France-Presse: “The mujahideen have left. They are really scared.”
However, Islamists seized the town of Diabaly, in government-controlled territory, on Monday.
When asked how long France’s intervention would last, France’s ambassador to Mali, Bernard Emie, replied: “We said weeks, but we said it’s going to be as long as necessary at the same time because we know it might be a bit more.”
Mali’s Foreign Minister Tieman Hubert Coulibaly said: “We cannot simply push [the rebels] back, we have to chase them away.”
On Monday, the UN Security Council convened in New York for an emergency meeting at France’s request.
UN Secretary General Ban Ki-moon said he hoped the intervention would help restore “Mali’s constitutional order and territorial integrity”.
France’s UN ambassador Gerard Araud said his country had the “understanding and support” of the 14 other Security Council members.
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.
Ansar Dine began pushing further south last week, seizing the town of Konna.
It has since been recaptured by Malian troops with French aerial support.
The battle for Mali