At least two people — a policeman and a civilian — were killed in a string of explosions and gunfire overnight Monday, with blasts and shootings heard as polls opened shortly after dawn in the capital Bujumbura, the epicentre of three months of anti-government protests.
Willy Nyamitwe, Nkurunziza's chief communications advisor, condemned the attacks as "terrorist acts" aimed at "intimidating voters".
Opposition and civil society groups have denounced Nkurunziza's candidacy as unconstitutional and a violation of a peace deal that ended a dozen years of civil war and ethnic massacres in 2006.
Around 3.8 million Burundians are eligible to vote between 06:00 (0400 GMT) and 16:00 (1300 GMT).
UN Secretary General Ban Ki-moon urged calm, calling on all sides to "refrain from any acts of violence that could compromise the stability of Burundi and the region."
Critics fear a win by the incumbent will be a hollow victory, leaving him ruling over a deeply divided nation.
"Despite a facade of pluralism, this is an election with only one candidate, where Burundians already know the outcome," said Thierry Vircoulon from the International Crisis Group, a think-tank that has warned the situation has all the ingredients to kick-start renewed civil war.
With the elections denounced by the opposition as a sham, the 51-year-old president — a former rebel, born-again Christian and football fanatic — is facing no serious competition.
Anti-Nkurunziza protests have been violently repressed, leaving at least 100 dead since late April.
Independent media has been shut down and many opponents have fled — joining an exodus of over 150,000 ordinary Burundians who fear their country may again be engulfed by widespread violence.
Doctors Without Borders (MSF) said Monday around a thousand people were fleeing each day into Tanzania, crossing the border "through the forest ... many travelling in the dark on foot and without belongings."
In mid-May, rebel generals attempted to overthrow Nkurunziza in a coup. After that failed they launched a rebellion in the north of the country.
Last-ditch crisis talks mediated by Uganda broke down on Sunday.
"The government has opted to isolate itself and go ahead with pseudo-elections," said Leonce Ngendakumana, a prominent opposition figure, after talks collapsed.
"They have refused to save Burundi from sliding into an abyss," said another opposition figure, Jean Minani.
A poor and landlocked former Belgian colony, Burundi is situated in the heart of central Africa's troubled Great Lakes region.
Analysts say renewed conflict in the country could reignite ethnic Hutu-Tutsi violence and bring another humanitarian disaster on the region.
The conflict also risks drawing in neighbouring states — much like in the war-torn east of Democratic Republic of Congo.
The last civil war in Burundi left at least 300,000 dead.
Nkurunziza's CNDD-FDD party scored a widely-expected landslide win in parliamentary polls held on May 29 that were boycotted by the opposition and condemned internationally as neither free nor fair.
UN electoral observers — the only international monitors in Tuesday's polls — said the last round of voting took place in a "climate of widespread fear and intimidation."
The results of parliamentary polls took a week to be announced.
The presidential elections are likely to be seen in the same light, diplomats said, meaning Nkurunziza — whose nation is heavily aid-dependent — will probably also face international isolation.
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