Burundi's authorities were counting votes on Tuesday, a day after holding a parliamentary election that was boycotted by the opposition and marred by sporadic gunfire and blasts.
The U.N. refugee agency UNHCR said nearly 10,000 fled over the weekend before Monday's vote, with some trekking through the bush after Burundi closed its borders, determined to escape its worst political crisis since civil war ended in 2005.
The European Union and African Union did not send observers to watch Monday's poll, saying conditions were not in place to ensure a fair vote.
The United States said it was disappointed that the government did not heed calls to delay the vote due to weeks of unrest triggered by President Pierre Nkurunziza's bid for a third term in office. Opponents said the bid is unconstitutional.
The government said it will not again postpone the presidential vote set for July 15 after it was pushed back several weeks. It says the parliamentary vote went smoothly and that next month's election will be the same.
The electoral commission CENI was expected to announce results on Wednesday or Thursday, spokesman Prosper Ntahogwamiye told Reuters, adding he did not have figure for the turnout yet.
But there was little doubt about the outcome given the opposition boycott.
Nkurunziza's CNDD-FDD party dominated the outgoing parliament with 81 of the 106 seats and was expected to secure another majority this time.
Although the opposition coalition did not campaign and boycotted the race, names of the parties were still on the ballot paper. A CENI official told state radio their votes would be counted and they would be awarded any seats they won.
The deputy president of opposition party Frodebu, Frederic Bamvuginyumvira, said Monday's parliamentary vote and local council polls held at the same time were a "non event."
"These elections were held in unacceptable conditions, were not inclusive, fair and democratic," he told Reuters.
Thousands flee violence
Weeks of unrest has prompted almost 144,000 Burundians, equivalent to more than 1 percent of the population, to flee to neighboring states.
UNHCR chief spokeswoman Melissa Fleming said Burundi closed its borders on Sunday before the vote.
"As of now and in the last 48 hours, refugees and people fleeing have been resorting to fleeing across informal border crossings through the forest to leave the country," she told reporters in Geneva.
Dozens of people were killed in clashes between protesters and police in protests that erupted after Nkurunziza's bid for another five year's in office was announced.
The president, who led a rebel group of the Hutu majority against forces against forces commanded by the Tutsi minority in the civil war, has rejected calls to withdraw his presidential bid, citing a court ruling saying he was allowed to run again.