Opposition supporters with a military escort entered the existing prime minister's office on Saturday without meeting any resistance.
They proclaimed Monja Roindefo Zafitsimivalo as the new prime minister.
Solo Ramarolahy, a journalist who works for Radio Madagascar, told Al Jazeera the situation in Antananarivo, the capital, was "confusing".
She said there was "no clue or any sign from the ruling regime" as to what they would do after Rajoelina gave the president an ultimatum of four hours to step down.
Thousands of anti-government demonstrators gathered in the city's central square and security was high for the protest, with the army present on surrounding streets.
Protests have occurred across Madagascar since January, with Rajoelina leading citizens against what he calls Ravalomanana's dictatorship.
The Reuters news agency quoted an unnamed presidential aide as saying that those occupying the prime mnister's office were not "vested with the power given by the people, through a democratic vote".
"This is and remains a street protest, using fear and repression to survive," the aide said.
|Protests against Ravalomanana have been held since the start of the year [AFP]
Earlier, Zafitsimivalo Monja said that elections would be be held within a year.
"We commit to organising presidential, parliamentary and district elections, in not more than 24 months," Monja said.
"We state that the president of the republic is no longer in a position to exercise the role allocated to him by the constitution and that it is clear the armed forces refuse to obey the president," he told the assembled journalists.
Earlier this week, Ravalomanana admitted to making some mistakes during the political crisis, in which over 100 people have been killed.
The killings happened after security forces were ordered to crack down on anti-government protests.
The security forces appear to have increasingly turned against Ravalomanana as pressure grows for him to step down.