The power struggle has brought weeks of riots, protests and looting
Madagascar opposition leader Andry Rajoelina has asked security forces to arrest President Marc Ravalomanana, after snubbing his referendum proposal.
Mr Rajoelina, a 34-year-old former DJ, said he knew what the people wanted and added he was impatient to take office.
The African Union condemned this as an "attempted coup d'etat" and called on Madagascar to respect its constitution.
Protests, looting and a mutiny has resulted from the unrest that has left at least 100 people dead since January.
The BBC's Jonah Fisher in Antananarivo says Mr Rajoelina has wrapped himself in the cloak of democracy, but he wants to replace an elected head of state without going to a ballot.
Earlier the army denied responsibility after two suspected mortar shells landed not far from the presidential palace.
A spokesman for the president said the blasts had been designed to intimidate his supporters.
On Monday, President Ravalomanana told a cabinet meeting he would only step down "democratically".
He also revealed the question for his proposed referendum to settle the crisis would be: "Do you accept for the current president of the republic to complete his mandate as provided by the constitution?"
Mr Ravalomanana, who was democratically re-elected for a second term in office in 2006, has previously said he wants to remain in office until his mandate expires in 2011.
But the opposition leader rejected the plebiscite plan and called for the president to be arrested.
He said earlier: "The people are thirsty for change and that's why we won't have a referendum and will put our transitional government in place."
Our correspondent says it is now up to the security forces to decide what happens next - but it is not an easy choice.
He adds they must decide whether to throw in their lot with the flashy young opposition leader or remain loyal to the embattled but democratically-elected president.
Mr Rajoelina says the president is a tyrant who misspends public money.
But Mr Ravalomanana's supporters say his rival is a young troublemaker who has not offered any policy alternatives.
Under President Ravalomanana, Madagascar's economy has opened up to foreign investment, particularly in the mining sector.
But 70% of the 20 million population still lives on less than $2 (£1.40) a day and correspondents say the opposition has tapped into popular frustration at the failure of this new wealth to trickle down.