"
[The rebels] opened fire on us - we fired warning shots and then they use heavy weapons
"
French army spokesman
A rebel group encountered a heavily armed contingent of the French Foreign Legion based in the western town of Duekoue.
The rebels say they did not intend to attack the French position and were chasing the Ivory Coast army.
The BBC's Paul Welsh in Ivory Coast says Saturday's clash marks a change in the role of French troops, whose official role is to protect foreign nationals and enforce a truce in the country's three-month-old civil war.
Rebels belonging to the Popular Ivorian Movement for the Far West (MPIGO) had been advancing on government-held positions, taking the town of Man on Thursday and pushing further south on Friday.
Saturday's clash occurred on a dirt road just outside Duekoue - a strategically important city, where two major roads from the north and the west meet and head to the capital Yamoussoukro.
The rebels say they were pursuing Ivorian troops who had cover behind the French lines - and that the French fired first.
However the French military denied this.
"They opened fire on us," an army spokesman told Reuters news agency. "We fired warning shots and then they use heavy weapons."
Quagmire?
It is unclear how many rebels have died, but there were no French injuries.
France, which has more than 1,500 troops currently in Ivory Coast, was initially mandated as a buffer force to maintain a fragile ceasefire signed on 17 October, between the government troops and the Ivory Coast Patriotic Movement (MPCI) rebel group.
However in recent weeks new rebels groups have emerged in the west of the country and have not entered peace talks.
The French say there has been no change in their policy in Ivory Coast - that they are continuing to protect foreigners and enforce the cease-fire with the MPCI.
But our correspondent says that in reality, the battle marks a change the French have finally been sucked into war.
UN condemnation
The United Nations Security Council condemned the rebels earlier on Saturday, for attempting to overthrow Ivorian President Laurent Gbagbo.
In its first intervention since the conflict began three months ago, the Security Council said it was gravely concerned about the consequences of the fighting, for both the country and the wider region.
It also praised the French for sending troops into the region.
Ivory Coast rebels began their uprising in September, spearheaded by an army revolt.
The country - the world's largest cocoa producer and previously seen as a beacon of peace in the troubled region - has now been divided in two, with rebels controlling the largely Muslim north.