Forces loyal to Ivory Coast presidential claimant Alassane Ouattara launched a heavy attack on the residence of incumbent leader Laurent Gbagbo on Wednesday, but were repelled.
Mr Ouattara has been officially recognised as the winner of the presidential elections in November last year, however Mr Gbagbo has refused to cede power and remains in hiding in his residence in Abidjan.
Fighting died down in the afternoon and forces loyal to Mr Ouattara had regrouped, Reuters reports, citing a Western military source who lives near Mr Gbagbo's residence.
Residents around the presidential palace in the Cocody neighbourhood had earlier reported hearing heavy gunfire and loud explosions coming from the direction of the palace.
It was the third straight day of fierce fighting in the economic capital.
Negotiations to persuade Mr Gbagbo to quit suffered a setback when he resisted pressure from the United Nations and France to sign a document renouncing his claim to power.
The French military said its troops were not involved in the attack, unlike earlier in the week when French and UN helicopter airstrikes backed the rebels' advance into Abidjan.