Madi said the president's dismissal of the government and election board on Friday was "antidemocratic and anti-constitutional," and tantamount to "a coup d'etat."
Tensions rose after Gbagbo sacked the head of the independent election commission amid accusations he was behind an attempt to add nearly 500,000 illegitimate voters onto the rolls.
Opposition supporters accused the ruling party of trying to disqualify voters who are not allied with Gbagbo.
Gbagbo asked Prime Minister Guillaume Soro to stay on to form a new government. Soro was the senior rebel leader before a 2007 peace deal ended the country's brief civil war and established the now-defunct government.
A spokeswoman for the opposition RDR party said Gbagbo's dissolution of the government was a step toward dictatorship.
"We cannot let this dictatorship establish itself," Anne Ouloto said.
The independent PIT party, allied with neither the opposition nor the president, also condemned the move.
"It runs in the face of all the peace accords we've signed since 2004," party secretary general Francois Kouablan said.
"That today the president thinks he has the powers to do this gives the impression that we've gone back 20 years."
At the heart of the impasse delaying a presidential vote is the question of who is really Ivorian.
While officially the vote is expected to take place before early March, the current political disarray casts doubt on this schedule.
The UN Security Council called recently for the election to be held before June.
Security forces were on alert in the divided West African country, but the situation appeared calm, including in the seaside commercial capital of Abidjan.
Ivorian newspapers described the announcements as a blow for the opposition, which held a number of posts in the former government and dominated the election commission.
"The head of state has administered an uppercut to the opposition," wrote the independent Soir-Info.
It forecast a new government "composed entirely of the presidential majority and FN," the ex-rebels of Soro.
For the country's two main opposition newspapers, Le Nouveau Reveil and Le Patriote, Gbabgo's announcements amount to "tearing up" the 2007 peace agreement clinched with Soro and aimed to unify the country.
Before its brief civil war, Ivory Coast was one of Africa's economic stars boasting a modern, cosmopolitan capital which lured tens of thousands of immigrants from poorer neighboring nations.