The deaths, which leading human rights activist Pierre-Claver Mbonimpa confirmed, brought the death toll in more than a week of protests to at least 13, including two soldiers and a policeman.
The small central African country has been rocked by violent protests since the ruling CNDD-FDD party designated Nkurunziza, a former rebel leader and born-again Christian from the Hutu majority, as its candidate in a presidential vote due to be held on June 26.
Police spokesman Liboire Bakundukize said 15 officers were wounded today after a grenade was "thrown by protesters", while others were wounded by rocks hurled by demonstrators.
An AFP reporter saw at least eight people with bullet wounds, with Burundi's Red Cross saying 46 were wounded.
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The police fired tear gas and hurled stun grenades in a bid to disperse the crowds.
"I am killed by Nkurunziza!" one injured man screamed, as he was taken to hospital with a bullet wound in his shoulder.
After a weekend truce, hundreds of protesters gathered today in a suburb of the capital Bujumbura, shouting at police who have for days blocked roads to prevent demonstrators from moving into the centre of the city.
Nkurunziza has been in power since 2005. His supporters say he is eligible to run again, since his first term in office followed his election by parliament -- not directly by the people as the constitution specifies.