Polling stations had opened early on Monday and about 3.8-million people had been expected to vote in the country’s controversial parliamentary poll, according to the electoral commission.
However, turnout was low in and around the capital city of Bujumbura, partly because the election was boycotted by 17 opposition groups.
The electoral commission expects the results to be announced within three days, but it declined to comment on the turnout.
The AU and the UN have also urged that next month’s presidential election be delayed, but Nkurunziza has insisted that the vote will go ahead as scheduled on July 15.
Burundi has been in turmoil since April, when Nkurunziza said he would seek a third term, triggering weeks of protests, and an abortive military coup last month.
Nkurunziza’s opponents say his decision to stand again violates the constitution as well as a peace deal that ended a civil war in 2005.
Nkurunziza has cited a constitutional court ruling saying he can run again, although the court’s vice president, another of those who have fled, said he and others had been pressured to rule in favour of Nkurunziza.
Dozens, including an opposition leader, have been killed in months of unrest, and the UNHCR, the UN refugee agency, says 127 000 have fled the country.
“They were thinking there is insecurity, they were thinking the situation in Burundi is not conducive for free and fair elections.
“But finally we proved to them that we can organise elections and secure elections,” said Willy Nyamitwe, spokesperson of the president.
A voter named Niyongabo Bienvenu told the Associated Press: “As a citizen of this country, it is my right to vote.
“And if you vote, you get the leadership that you want.
“You get the chance to make the changes that you want.”
Meanwhile, the international community fears the election will only make matters worse – destabilising Burundi and a wider region beyond its borders.
The AU withheld its monitors in a gesture of denying the legitimacy of the election results. It also hinted at further actions.
“Once the elections take place in complete defiance of the African Union and the international community, I guess the organs won’t sit and will make proper calls when the time comes,” said Jacob Enoh Eben, spokesperson of the AU Commission.
The US is “deeply disappointed” in Burundi’s decision to go through with parliamentary elections on Monday despite calls for a postponement, the State Department said.
Spokesperson Mark Toner told reporters there were “woefully inadequate conditions for free and fair elections” in the central African nation.
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