"We must follow democratic principles. If we have to, we will organise a referendum," he said.
The BBC's Jonah Fisher in Antananarivo said Mr Ravalamanana's offer was an indication of how much pressure he was under from the opposition, led by the capital's former mayor, Andry Rajoelina.
It was not immediately clear what the content of the proposed referendum would be, but the president's special advisers told the BBC it would be along the lines of whether Mr Ravalamanana should remain in office.
Mr Rajoelina had said earlier that he was in "permanent contact" with the army and giving them orders.
But our correspondent says there appear to be divisions within the military, with some elements joining calls for the president's resignation and others deeply opposed to Mr Rajoelina's ambitions.
Mr Ravalomanana, democratically elected to a second term in office in 2006, has described the opposition movement as an undemocratic street protest which "uses terror and repression to survive".
The crisis has hurt the country's economy. Its tourist industry, worth nearly $400m (£290m) a year, has now had two months with no revenue.
Under President Ravalomanana, Madagascar's economy opened to foreign investment but 70% of the nation's 20 million population still live on incomes of less than $2 (£1.40) a day.
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