The meeting in Ivory Coast's main city Abidjan on Saturday comes after Malian soldiers, backed by French troops and air power, retook a key central town from rebels swooping down from their northern stronghold and threatening the capital Bamako.
France, who began the military operation after the central town of Konna fell to Al Qaeda-linked fighters on January 11, will be represented by foreign minister Laurent Fabius.
"We will see with our African friends how we can speed up the deployment of MISMA [International Mission for Mali Assistance]," he said on arrival in Abidjan.
"France was obliged to intervene very, very rapidly, otherwise there would have been no more Mali.
"But it is well understood that it is the Africans that must pick up the baton."
Mr Fabius says the African force will be ready in weeks.
France has already put nearly two-thirds of the 2,500 troops it has pledged on the ground in Mali, amid fears that the vast arid north which the rebels control could become a haven for Islamist militants and threaten security both in the region and overseas.
US defence secretary Leon Panetta hailed the French role and expressed the support of Washington, which has offered to send transport planes and share intelligence.
"We will continue to work with countries in that region and we will try to continue to assist France in the efforts they have conducted," Mr Panetta told BBC in an interview.
"We commend France for taking the step to try to block the AQIM and we will try to assist them as do other countries in that effort," he said, referring to the Al Qaeda in the Islamic Maghreb.
The Economic Community of West African States (ECOWAS) has vowed to boost the French effort with a total of about 5,800 troops. But only about a 100 have actually reached Mali.
Oil-rich Chad, whose battle-hardened soldiers are experienced in fending off rebel attacks on their territory and have been deployed in neighbouring countries such as the Central African Republic, has promised 2,000 troops.
Regional powerhouse Nigeria subsequently promised to boost its troop allotment for Mali from a planned 900 to 1,200 soldiers.
Chadian leader Idriss Deby Itno is attending the summit along with Mali's interim president Dioncounda Traore.
"The war has been forced by the refusal of the criminal movements and terrorists of the offers of peace," ECOWAS president Desire Kadre Ouedraogo said, highlighting the urgency to "accelerate the deployment of MISMA".
The office of the president of Burkina Faso, Mali's south-eastern neighbour, said the summit will "review the security situation before charting out new directions for the speedy deployment of west African troops".
The African deployment follows a United Nations resolution.
It was originally envisaged that Western powers including France would provide logistical support to an African-led force, but it is now clear that French troops will be at the frontline of operations.
The French presence has been a life saver for Mali's ill-equipped and demoralised soldiers, struggling to fight an amalgam of Islamists and Tuareg rebel groups.