Guillaume Soro, the man designated by Ouattara as prime minister, said the country should stand together in the spirit of Tunisian and Egyptian citizens and demand Gbagbo hand over power.
He added that rebel army forces in the north of the country where Ouattara draws his support are "ready to help" end Gbagbo's tenure, Bloomberg News quoted him as saying.
"We will not be fighting independently," he added. "We will organize one united army, and that's what we're in the process of doing."
The election in November was meant to unite a country divided by civil war in 2002. Soro said political conflicts since the election have cost 500 lives in the country.
The United Nations and leaders from the African Union warn that the situation in the Ivory Coast was on the brink of civil war once again.
Ouattara is holed up in a hotel in Abidjan surrounded by U.N. peacekeepers.