Now 3,150 French soldiers have been assigned to the French mission, dubbed Operation Serval. At least 2,150 of them are on Malian territory, the French have said.
The government is considering sending more troops, it said Monday.
The Islamists are well-equipped and well-trained, French officials have said. But advances made by the Malian army toward cities that the Islamists previously controlled "constitutes a certain military success for the Bamako government and for French forces," said French Defense Minister Jean-Yves le Drian.
"I reaffirm my total confidence in our soldiers who are in combat with determination in the mission decided by the French president." he said. "It aims to restore sovereignty to Mali on its territory and to prevent the risk of the constitution of a terrorist sanctuary in the heart of Africa."
Rebel control over Diabaly was one of the chief concerns to Mali and France as they tried to stop the Islamists' movement into the south.
French and Malian forces retook Konna from militants Friday, a French source said. But gunfire could still be heard there on Monday.
As fighting continues, many people are being cut off and are in need of basic supplies.
The U.N. Security Council in December authorized the deployment of an African-led International Support Mission in Mali, and West African leaders met Saturday in Ivory Coast to discuss speeding up deployment of troops.
The regional bloc -- the Economic Community Of West African States -- has said it has 3,300 regional troops on standby.
It urged the United Nations to provide immediate logistical and financial support for African troops.
"The escalation of conflict in recent days reminds us of the importance of assuming our responsibilities very quickly in a dynamic of coordination with our partners," said Charles Koffi Diby, the Ivory Coast foreign minister. "We should act very quickly."
'It was absolutely necessary'
Despite its unilateral decision to get involved, France is seeking help from its regional allies and the international community.
Christian Rouyer, French ambassador to Mali, reiterated the need for the French offensive in Mali.
"We had a friendly country that was on the verge of dying," Rouyer said Friday. "It was absolutely necessary to act with urgency. We did it, I believe, with full knowledge of the reasons."
Leaders from several countries have offered troops or logistical support.
The European Union has approved a training mission. Canada and Britain are deploying military transport aircraft. Nigeria is set to deploy soldiers as part of the U.N.-mandated African force to fight the insurgents.
No military aid from U.S.
U.S. policy prohibits direct military aid to Mali because the fledgling government is the result of a coup. No support can go to the Malian military directly until leaders are chosen through an election, said Victoria Nuland, a State Department spokeswoman.
So far, the United States has only shared intelligence from intercepted signals and satellites with France, defense officials said.
U.S. trainers will be in African nations to prepare forces set to be deployed in Mali. Trainers will be in Niger, Nigeria, Burkina Faso, Senegal, Togo and Ghana.
The United Nations is warning of a record number of Malians fleeing to neighboring nations.
The violence could soon displace up to 700,000 in the country and around the region, said Melissa Fleming, a spokeswoman for the U.N. refugee agency.