Some 2,000 people heard Rajoelina, 34, speak at a rally on Tuesday. He demanded that Ravalomanana step down by Saturday.
"If there is no reply or peaceful solution from the president, then we will put in place a transitional government," he said.
Ravalomanana responded by saying that he is still in charge and called for calm.
Rajoelina was democratically elected as mayor but his sacking is legal, one expert said.
"The government's move is legal if it feels the mayor is not fulfiling his mandate," Jean-Eric Rakotoarisoa, a constitutional law expert, said.
"However, putting the move in place will be more difficult because it will be contested by the people of Antananarivo who are behind the mayor."
Rajoelina has used broadcast stations owned by him to urge Ravalomanana to resign.
His TV station was temporarily shut down by the president last week, leading to large rallies which turned into rioting and looting, leaving dozens of people dead.
More than 100 people have died in the chaos, according to the US envoy to the country.
Police say that 76 people have died during the unrest.
The African Union has said that it will not support any attempts to overthrow Ravalomanana, a self-made millionaire, from power.