Mali’s neighbours are considering imposing an economic blockade to force its military leaders to step down, after rebels seized the whole of the north over the weekend.
West African leaders had given Mali’s junta until Monday to leave power or face sanctions.
The army said it had staged its coup because the campaign against the Tuareg rebels had been poorly run.
But the Tuareg fighters have responded by making rapid advances.
After seizing the historic city of Timbuktu on Sunday, rebel spokesman Moussa Ag Assarid told the BBC that his forces had no intention of moving south, towards the capital, Bamako, but would consolidate their control of the areas they had seized.
His National Movement for the Liberation of Azawad (MNLA) group wants independence for the Tuareg’s northern homeland, which it calls Azawad. Other rebel forces in the north have recently joined forces with Islamist militants in the region.
Former colonial power France has advised its nationals “whose presence is not essential” to leave the country - including those in Bamako.
There are around 5,000 French nationals in Mali, the AFP news agency reports.
‘Build a nation’
Coup leader Capt Amadou Sanogo has asked for international help to fight the rebels, whose ranks have also been swelled by well-armed fighters returning from the conflict in Libya, where they backed former leader Muammar Gaddafi.