It remained unclear who was in charge of the country after an earlier announcement by the army that it had taken control, dissolved parliament and would put in place a transitional government.
Opposition figures said around 30 people had been killed and 100 injured as tens of thousands took to the streets in protest against plans to allow Compaore to extend his long reign.
Hundreds stormed parliament and other public buildings including the national television headquarters in the capital Ougadougou, ransacking offices and setting fire to cars despite a heavy police and army presence.
Compaore initially called a state of emergency but appeared on television just a few hours later to say it had been called off.
"I have heard the message," the president said.
But he refused to step down on Thursday, saying instead that he was "available" for talks on "a period of transition after which power will be transferred to a democratically elected president".
At a hastily assembled press conference earlier in the day, the army said it was imposing a dusk-to-dawn curfew. It pledged to restore constitutional order within 12 months.
The communique, read out by an officer, was signed by the army chief of staff Nabere Honore Traore.

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