One Abidjan resident said that youths there had set fire to a bus and shops had closed.
Police used tear gas to disperse the protesters, who had also turned out in several cities and towns on the previous Thursday.
Protests were triggered by a dispute between Gbagbo and Banny over their powers under a UN-backed peace deal for the West African country that hopes for elections within a year.
The dispute was over the reinstatment of three senior civil servants accused of negligence when toxic waste was dumped in Abidjan in August. Ten people were killed by the fumes.
"[Gbagbo] has restored assassins from the toxic waste affair. Ivorians cannot accept that"
Kouadio Konan Berti
The three had been suspended during an investigation ordered by Banny, who has received the support of UN and foreign mediators.
Kouadio Konan Berti, an opposition youth leader, said: "[Gbagbo] has restored assassins from the toxic waste affair. Ivorians cannot accept that.
"We have asked people to take to the streets. For a while the action of the government has been blocked with Gbagbo on one side and Banny on the other."
Two previously scheduled election deadlines in Ivory Coast, a former French colony which was once a prosperous West African country, have already passed as internationally backed peace efforts were impeded by political complexities.
Diplomats say they fear the latest row could further delay the elections, which requires progression on sensititve issues such as disarmament and an identification process to determine who is eligible to vote.