The army dissidents have refused government orders to crack down on opposition protests.
The security forces' support for Ravalomanana began to waver last month, after they opened fire and killed at least 25 pro-Rajoelina demonstrators.
General Edmond Rasolofomahandry, then head of the army, gave the government a 72-hour ultimatum to resolve the political standoff or face military intervention, but was then replaced as army chief after "negotiations" among senior officers.
The opposition camp appeared to endorse the army mutineers for the first time on Wednesday, praising them "for not wanting to disgrace their military honour through acts of repression".
But it is unclear whether the faction of the army that has mutinied is preparing to throw its support behind the Rajoelina, the sacked mayor of Antananarivo, who has been spearheading the anti-government protests.
Ravalomanana urged the army on Thursday to remain neutral in an address on national radio.
"Our priority is restoring order," he said. "I'm calling on the security forces to live up to their responsibilities and protect the people ... and their property."
The leaders of the co-operating army, paramilitary and police force in charge of security in the capital have said that they will work together to stop looting, but said they were no longer taking orders from the president.
Gal Pily Gilbain, the commander of the paramilitary element in the capital force, used state radio to urge his troops to stay out of politics and politicians to "apply themselves to resolving the crisis".
Ban Ki-moon, the UN secretary-general, has called for dialogue between the two rivals.
|Rasolofomahandry was replaced as
army chief [AFP]
"The only solution to the current crisis is the resumption of dialogue," Michele Montas, a UN spokeswoman at the UN headquarters in New York, quoted Ban as saying.
"While there is concern over divisions within the armed forces, he [Ban] welcomes the decision by the armed forces to continue to respect constitutional order."
A three-day national conference organised by church leaders, scheduled to start on Thursday, was postponed indefinitely after Rajoelina, who has been under UN protection since fleeing attempts to arrest him last week, refused to attend.
Rajoelina has accused the president of running a dictatorship. Ravalomanana has admitted that he made mistakes over the crisis and has said he is open to a negotiated settlement.