On Saturday Ivorian warplanes killed nine French soldiers in an attack.
"President Gbagbo bears a heavy and personal responsibility in all of this affair," French Foreign Minister Michel Barnier said on Sunday.
He was speaking as French ministers said there were no immediate plans to evacuate the estimated 14,000 French nationals living in the Ivory Coast, a former French colony, after clashes between government and French forces.
Mob violence targeting foreign residents was reported overnight in the economic capital Abidjan, including the looting of homes and businesses.
Controlled but tense
"The situation is under control but remains tense, we must not deny it," Defence Minister Michele Alliot-Marie said.
Four schools were looted and
torched as violence continued
Interior Minister Dominique de Villepin told a French radio station that the evacuation option was not "an immediate issue" but said it was important that Gbagbo "retakes control, today, of the people in the street".
"The first priority is to ensure the safety of our French [citizens]," de Villepin said, adding that it was vital to avoid any further complications.
But France's military chief said on Sunday that his troops may have killed or wounded people during recent clashes with anti-French demonstrators.
The chairman of the Joint Chiefs of Staff, General Henri Bentegeat, said casualties were inflicted while trying to protect foreign residents in Abidjan.
"We had to fire warning shots and we could indeed have wounded or killed a few people," he said.
"We at all times made every effort to limit to a minimum the risks both for the civilian population and for any adversaries we came across," he told France's TV5.
"We had to fire warning shots and we could indeed have wounded or killed a few people"
General Henri Bentegeat, chairman French Joint Chiefs of Staff
He said his troops had rescued 750 people, mainly French nationals but also Lebanese, Belgians and Germans who were caught up in the violence.
"We faced a number of looters in Abidjan when we went to the aid of French nationals - in all we have taken in 750 people," Bentegeat said, adding that he was proud of the attitude of his men.
Although France has reinforced its military capacity with the dispatch of more troops, totalling about 660, it maintains that "the only solution is a political one and the future of Ivory Coast lies with a political settlement", he said.
For that to happen "good sense has to return and one has to stop imagining that a solution can be achieved through force. People have to calm down, it is time to act responsibly", he added.
In a radio and television interview on Sunday, Barnier said the French-brokered Marcoussis peace accords of January 2003 were the only alternatives to violence in Ivory Coast.
Pursuing diplomatic pressures on its former African colony, France floated a UN draft resolution late on Sunday, calling for an arms embargo against the Ivory Coast, freezing of assets and a travel ban against people accused of blocking the peace process.