It is not clear who was behind the attack on the RDR office
The violence broke out despite a night-time curfew, as a deadline passed to release the results of Sunday’s presidential election run-off.
Supporters of President Laurent Gbagbo are preventing the results from being declared, saying there was fraud in the north, where Mr Ouattara is popular.
The election is the first for a decade.
It is intended to reunify the country, the world’s largest cocoa producer, divided since a 2002 civil war. Former New Forces rebels still control the north.
Mr Gbagbo’s spokesman said they would appeal to the Constitutional Court to annul the results from parts of the north.
The BBC’s Valerie Bony says there were large pools of blood in the courtyard of the office and blood-stained clothes and bullet holes in the offices.
The office of the RDR party that was attacked is in the Yopougon district in the west of Abidjan – seen as a pro-Gbagbo area.
BBC News, Abidjan
There were large pools of blood in the courtyard of the RDR office. In the offices, blood-stained clothes and bullet holes.
Filing drawers are upturned with paper scattered around.
There were around 50 RDR sympathisers spending the overnight curfew in the offices, watching the television in the hope of getting results.
Those who attacked were apparently looking for weapons.
The building was reportedly targeted by a group of armed men at 2300 local time (and GMT) on Wednesday night – just an hour before the deadline to release the election results.
“They climbed the walls and the door and at that point they started shooting at people,” an RDR official, who did not wish to be named, told the BBC.
He said some of the assailants were wearing civilians clothes, others in gendarme uniform.
“I saw three people lying down, and then they left them for dead. I’m devastated. It was a horrible atrocity and it was hard for me to take – to attack people in front of your own eyes, isn’t easy to watch.”
There has been no independent confirmation that gendarmes were linked to the attack.
Official from Mr Gbagbo’s FPI party say their local office was subsequently attacked in an apparent revenge raid.
Both the army and UN peacekeepers have been patrolling Abidjan’s streets since Sunday to prevent an outbreak of violence.
Other parts of Abidjan are reported to be quiet, with many people staying at home and many banks and businesses closed.
Both former colonial power France, the US and the UN have urged the Ivorian authorities to announce the results.
The UN mission says it has received reports of violence in parts of the west and north on election day, but that overall the voting seemed to be peaceful.
“Generally speaking, globally speaking, it went well, because all candidates, people were voting in a peaceful manner,” said UN spokesman Hamoudoun Toure.
On Tuesday evening, Mr Gbagbo’s representative in the electoral commission tore up the first batch of results as the commission’s spokesman was about to announce them.
Mr Ouattara’s supporters say the Gbagbo camp is blocking the announcement of the results because he has lost.
France retains close military and economic ties to its former colony, and on Wednesday, French Foreign Minister Michele Alliot-Marie said its forces would be able to intervene if French nationals or interests were affected by unrest in Ivory Coast.
Mr Gbagbo’s supporters have previously accused France of bias, and French targets in the country have been attacked.