Ouattara, who has been recognised as president by the international community, on Monday called on all citizens to stop work until Gbagbo stepped down.
"We should not let them steal our victory," said the RHDP party, in a statement signed by its director, Alphonse Djedje Mady.
But the statement came out late, and was not carried by the pro-Gbagbo state media.
RFI correspondent Marco Chown Oved said that in downtown Abidjan, the commercial capital, activity appeared normal, with shops opening for business.
“There were plenty of cars on the street and there was nothing to indicate the strike was being followed,” Oved said.
“But in the north of the country, in the rebel capital Bouake, it’s a complete ghost town. This area has sworn an allegiance to Ouattara.”
In Paris on Monday afternoon, the atmosphere was calm as Ouattara supporters made their way inside the Ivorian embassy.
The move came after Paris said it would recognise Ouattara's envoy over that of Gbagbo, who has clung on to power since the disputed 28 November vote.
Marcel Youpeh, who represents Ouattara's coalition in France, says that nothing was damaged, and that demonstrators had removed Gbagbo's photograph from the wall.
Reporting from the embassy, RFI’s Molly Guinness said police with riot shields were preventing the assembled crowd in the street from entering.
“I spoke to a man here who has a brother on the inside. He says the atmosphere is quite convivial. There are about 20 people. Some of them are women, and apparently no one is trying to get rid of them,” Guinness said.
The embassy in France is one of the West African country's most important diplomatic missions.
The move to recognise the new envoy came a day after French authorities grounded a plane belonging to Gbagbo at an airport in France in response to a request by the rival Ivorian government set up by Ouattara.
Gbagbo's next challenge will be a meeting Tuesday with leaders from Benin, Cape Verde and Sierra Leone, who come carrying a message from the Economic Community of West African States (Ecowas) that Gbagbo must step down.
Gbagbo branded the threat part of a Western plot directed by France and the United States.