A BBC reporter in the capital says dozens of people were queuing to vote in polling stations which saw hundreds lining up in local polls last month.
The opposition claimed those elections were rigged and pulled out of the presidential ballot.
The poll is the first since the last active rebel group agreed a ceasefire. But diplomats have warned that the country is still in danger of slipping back into civil conflict.
The election campaign has been marred by a series of grenade attacks which left at least five people dead and 60 injured – the most recent on Sunday night.
Agathon Rwasa, leader of the last active rebel group, was expected to be the main challenger to Mr Nkurunziza, also a former rebel leader.
But he has disappeared and is now thought to be hiding in neighbouring Democratic Republic of Congo, although his FNL group says he is merely “on holiday”.
BBC East Africa correspondent Peter Greste says the problems make the peace deal of 2006, which ended 13 years of civil war, look decidedly unstable.
The ruling FDD party has called on voters to turn out in large numbers, while the opposition has called on them to boycott the polls.
Forrás: BBC, Al Jazeera