More than 130 people have been killed in Madagascar's political crisis, most of them when security forces cracked down on anti-government protests at the order of Ravalomanana's government.
The security forces' relationship with the government has deteriorated as a result and a faction of the army has revolted, refusing to act against the opposition.
Rajoelina has several times said that he controls the army.
"Of course it is me who is giving the army orders. I am in permanent contact with them," Rajoelina was quoted by the Reuters news agency as saying on Sunday.
"Of course it is me who is giving the army orders. I am in permanent contact with them"
Andry Rajoelina, opposition leader
Despite his assertion, there has been no confirmation from the army that Rajoelina is giving orders.
Madagascar's army has remained traditionally neutral during various periods of political volatility since independence from France in 1960.
On Saturday, Rajoelina declared the president had just four hours to step down, but Ravalomanana, who was elected to a second term in 2006, defied the ultimatum and his supporters guarded the presidential palace through the night.
"For now we are waiting for him to resign," Rajoelina said in his interview with Reuters.
"If he doesn't, then we have other options ... I can't say if that means a military intervention."
Rajoelina said he expected important developments within the next day or two.
"We will let him leave quietly. I think the situation will evolve within the next 48 hours," he said.
Al Jazeera's Haru Mutasa, reporting from the capital Antananarivo, said that Rajoelina wanted the constitution court to impeach the president on Monday, accusing him of misuse of public funds.
"If they do this it will only make the situation in Madagascar even more tense, people are fearing there could be even more bloodshed," she said.
While Rajoelina has tapped into widespread public discontent, especially with high levels of poverty in Madagascar, many inhabitants are fed up with the disruption this year's protests and unrest have brought to their lives and the local economy.