Ouattara, the internationally recognized winner of last year's presidential election, has been gaining ground against incumbent Laurent Gbagbo, the BBC said, but Gbagbo holds Abidjan, the former capital and largest city.
Ouattara's fighters have been advancing in two offensives from their northern bases. In the west, they are reported to have captured Daloa and Duekoue, while in the east, they say they have taken the city of Bondoukou.
Gbagbo's spokesman said the army was staging tactical withdrawals.
The United Nations, which supports Ouattara, said young Gbagbo supporters are continuing to attack civilians in Abidjan. The youths are reportedly being enlisted in the army to replace soldiers who have deserted or defected.
Ouattara has lost patience with diplomatic efforts to persuade Gbagbo to cede power four months after losing the election.
"All the peaceful routes to lead Laurent Gbagbo to admit his defeat have been exhausted," he said in a statement released Tuesday.