Their offensive threatens to make a battleground of the city, the last stronghold of presidential rival Laurent Gbagbo.
Some police units and the head of the army have defected from Mr Gbagbo.
The UN says Mr Gbagbo lost last year's election to Mr Ouattara, but he has so far refused to cede power.
Armed supporters of Mr Gbagbo have been patrolling districts of the city, setting up roadblocks.
The BBC's Valerie Bony in Abidjan says there have been fierce clashes around the national television centre in a residential part of the city, and heavy weapons fire in northern suburbs.'Game over'
She says an informed source had told her that Edouard Kassarate, the head of the gendarmerie or military police, had defected to the Ouattara side and had gone to the Hotel de Golf, Mr Ouattara's headquarters in Abidjan, which had been besieged by Mr Gbagbo's forces.