The power struggle has brought weeks of riots, protests and looting
Madagascar's opposition leader has threatened to lead marchers to the presidential palace if President Marc Ravalomanana does not step down.
Andry Rajoelina, who emerged from hiding to address a mass rally in the capital, said the president should resign "humbly" within hours.
His followers have begun forming their own government.
But after the opposition's deadline passed, Mr Ravalomanana was still refusing to stand down.
"I am still president," he said after emerging from the presidential palace outside the capital, Antananarivo, to address hundreds of supporters.
An aide to Mr Rajoelina, who did not wish to be named, said after the deadline had passed that the opposition was still waiting for the president to quit.
"If we don't receive the call [from the president to say he has resigned], something will happen," the aide told Reuters news agency.
The BBC's Jonah Fisher reports that the opposition does not seem to have the appetite for a violent confrontation with the president and his supporters and prefer, instead, to keep turning up the pressure.
Nor, our correspondent adds, has there been any indication that the opposition would settle for a coalition with Mr Ravalomanana.
The Indian Ocean island nation has been rocked by seven weeks of riots, protests and looting which have left about 100 people dead.
The opposition leader - who was sacked by the government as mayor of the capital last month - went into hiding on 5 March after security forces tried to arrest him.
On Saturday, 5,000 of his supporters, clad in orange T-shirts and hats, gathered as Mr Rajoelina reappeared to speak at Antananarivo's 13 May Plaza.
"There is only one demand, that's the departure of Ravalomanana," the 34-year-old businessman and former DJ said.
"I, Andry Rajoelina, am ready to carry out the democratic handover of power."
He added that he was going to the presidential palace "to say goodbye".
Mr Rajoelina - who accuses the president of being a tyrant who misspends public money - has been trying to establish an alternative cabinet, with himself as president.
December 2006: Marc Ravalomanana returned as president for second term
31 January 2009: Opposition leader Andry Rajoelina says he is in charge of the country after weeks of bloody protests
3 February: Mr Rajoelina is sacked as mayor of Antananarivo
5 March: Mr Rajoelina goes into hiding
13 March: President Ravolamanana urges supporters to turn out and defend his authority
14 March: Mr Rajoelina re-emerges and gives president just hours to resign
On Wednesday, the leader of a widening mutiny within the army ousted the chief of staff and a day later the military police said it would no longer take orders from the government.
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.