Clashes were taking place in several parts of Bujumbura the day after the president launched a controversial bid to stay in power for a third term and despite a government ban on protests.
Independent eyewitnesses said one person was shot dead in the city's Ngagara district and another in Musaga after police used live ammunition to disperse crowds.
One body was left in the streets while another was taken away by Red Cross workers, several eyewitnesses said.
"We had called for peaceful protests and that is what happened, but the police and ruling party militia fired real bullets at the protestors," said a Burundian opposition leader, Frodebu Leonce Ngendakumana.
Local media reports added that several more people have been wounded in the city, while several police have also been hurt in stone throwing, AFP reported.
Burundi's Interior Minister Edouard Nduwimana condemned what he said were "uprisings called for by certain politicians and civil society".
Opposition figures and rights groups say the president's effort to cling to power is unconstitutional and could push Burundi -- which emerged from civil war in 2006 -- back into violence.