The military named a high-ranking officer, Isaac Zida, to lead the country's transition yesterday, a day after Compaore was forced to resign as plans to extend his 27-year rule exploded into violent demonstrations that saw parliament set ablaze.
Some have drawn parallels with the Arab Spring, with the developments closely watched across a continent where several other veteran heads of state are also trying to cling to power.
But opposition and activist leaders swiftly issued a statement warning the military against a power grab, demanding instead a "democratic and civilian transition".
"The victory born from this popular uprising belongs to the people, and the task of managing the transition falls by right to the people. In no case can it be confiscated by the army," they said in a statement.
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They called a new mass rally in the capital Ouagadougou today at the site now nicknamed "Revolution Square" where up to a million people had gathered earlier this week to demand Compaore's resignation.
Zida, the second in command of the presidential guard, said he had assumed "the responsibilities of head of the transition and of head of state" to ensure a "smooth democratic transition".
The transition will be carried out "together with the other components of national life," he said, referring to the political opposition and civil leaders.
The army's endorsement was signed by General Nabere Honore Traore, who initially said he would himself assume power, a claim Zida had dismissed as "obsolete".
Speaking on television yesterday, the military officer also said the ousted president was "in a safe place" and his "safety and well-being are assured".
In neighbouring Ivory Coast the presidency confirmed reports that Compaore, who left Ouagadougou on Friday according to French diplomats, was in the country.