"I will never resign," Ravalomanana told a church service attended by about 5,000 supporters outside his presidential palace.
"We have to follow the democratic process," he said, adding that he was ready to hold a referendum on the way forward for his nation of 20 million people.
Several thousand opposition supporters attended another church service in the downtown square that has become the focal point for anti-government demonstrations.
The African Union said it was concerned at escalating tensions in Madagascar, a poor Indian Ocean island known for its rare wildlife but riven by political upheavals. It reiterated appeals to the rivals to find a negotiated solution.
More than 100 people have died in political violence since January.
Ravalomanana has lost the backing of much of the military -- mainly because of anger that he ordered soldiers to fire at demonstrators. Ravalomanana's army chief of staff agreed to cede power last week to Andre Ndrianarijaona, who is believed to be sympathetic to the opposition leader but has so far remained out of the political power struggle.
Reacting to Rajoelina's claims that he now controls the military, army spokesman Noel Rakotonandrasana said soldiers would only approach the presidential palace if it was necessary to free roads blocked by pro-presidential supporters.
"Our main mission is first and foremost to re-establish order. And for that, we won't take orders from anyone," he told The Associated Press.
The opposition accuses 49-year-old Ravalomanana of abuse of funds and power and of being blind to the crushing poverty of his people.
The president says that Rajoelina -- a 34 year-old disc jockey who became mayor of the capital -- is a rabble rouser and his supporters are of street protesters who don't care about democracy.
Ravalomanana is no stranger to power struggles. He won a six-month battle of nerves in 2001, when the island was divided with two governments, two capitals and two presidents. Eventually his rival -- a longtime ruler of Madagascar -- went into exile in France.
He won elections in 2006, although opposition parties contested the result -- and the next elections aren't due till 2011.
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