African Union leaders continue to throw their weight behind Ouattara, who has a U.N. Security Council resolution recognizing him as the winner of a November presidential election.
The election was meant to unite a country divided by war in 2002 but clashes between rival camps are threatening to drag the country back into civil conflict.
French Foreign Minister of Alain Juppe told Europe 1 radio that pressure on Gbagbo is growing.
"Financial sanctions don't take a fortnight, they take several months," the minister said. "And today we can see clearly that Gbagbo is gradually being stifled."
Human Rights Watch in a chronicle of abuses in Ivory Coast said both sides are responsible for violence in the country, though forces loyal to Gbagbo might have committed human rights crimes during the conflict.
Juppe said he wasn't going to make any predictions on when Gbagbo would bow to growing international pressure but added his country would "do everything" to make sure Ouattara exerts power.
"That's what is gradually happening in Ivory Coast," he said.
Ivory Coast gained independence from France in 1960.