Mr Ouattara is recognised internationally as the winner of a November election. But his rival, incumbent President Laurent Gbagbo, has refused to concede that he has lost.
Residents in Abobo reported heavy gunfire after at least 30 trucks of security officers loyal to Mr Gbagbo and several armoured vehicles surrounded the area at dawn. Witnesses said at least two members of the security forces had been killed, though the reports could not be independently confirmed.
Some reports cited the presence of armed civilians who exchanged fire with the police.
A spokesman for the New Forces - the armed movement that is loyal to Mr Ouattara and that controls the northern half of the country - said they were not involved. UN peacekeepers who tried to enter an area of Abobo known as PK18 were turned back, reports say.