Voter turnout on Monday was estimated at 65%, said the head of the United Nations Operation in Burundi (ONUB), Carolyn McAskie.
"Turnout is slightly lower than in municipal elections" which were held on 3 June when it was 80%, she told a news conference in the capital, Bujumbura.
The ONUB earlier said the turnout was comparatively low because of fear from insecurity during the 3 June elections in which grenade attacks and gunshots killed one person and injured more than a dozen others, including a UN peacekeeper.
In the first serious incident during the legislative polls, a Burundian soldier was slightly injured when a hand grenade exploded near a Bujumbura polling station late on Monday as vote counting began shortly after its closure.
"Unidentified people threw a hand grenade near the polling station where ballots were being counted in the Kinama district," the deputy chief of Burundi's police Colonel Helmenegilde Mimenya told AFP.
"Apparently, they wanted to stop the vote counting, but soldiers moved in very quickly and made the area safe," he said.
Ballot boxes were taken to an unidentified place where the counting is to continue, he added.
President Domitien Ndayizeye's
party lost the municipal elections
McAskie said that reports of fraud were "not sufficient ... to affect the overall result".
Ahmedou Seck, a spokesman for the ONUB, told reporters that several incidents of fraud had been reported in the tiny Central African nation but said they did not appear serious enough to affect the results.
Witnesses said President Domitien Ndayizeye's Front for Democracy in Burundi (FRODEBU) party, which lost the municipal vote, was primarily involved in fraud, allegations that the party dismissed.
"I saw an employee of (FRODEBU spokesman) Jean de Dieu Mutabazi distributing cards near his house on Monday," a radio journalist, Louis Kamwenusuba, told AFP.
Paul Ngarame, head of the National Independent Electoral Commission, confirmed the agency had received the claim and had asked the court to summon Mutabazi, who described the accusation as "false machinations aimed at confusing voters".
As voting closed, National Independent Electoral Commission spokesman Astere Kana said gunshots were heard in Bujumbura Rural and Bubanza provinces, to the west of the capital, which were the centre of violence in the local polls.
Voting was delayed for hours in one polling station in the two powderkeg provinces that are prone to attacks by the country's lone remaining Hutu rebel group, the National Liberation Forces (FNL).
But an FNL statement said the group's leader Agathon Rwasa had ordered its fighters not to intimidate voters or disrupt the election, which it said went ahead without major incidents.
Preliminary results are expected overnight on Monday, officials said.
Many voters said they hoped the ballot would help end more than a decade of ethnically driven civil war that has claimed 300,000 lives.
Monday's legislative elections saw 3704 candidates from 25 political parties, of which six are former rebel groups, as well as 15 independents battle it out in the country's 100 constituencies.
Voters queue up for the 3 June
election, in which turnout was 80%
Lawmakers elected in Monday's polls will be joined by senators picked by municipal councillors on 29 July to elect the country's first post-transitional president.
The former main Hutu rebel group, Forces for the Defence of Democracy (FDD), can be sure of a majority in the upper house after a sweep of the municipal elections.
Analysts have predicted that the FDD will win the elections and its leader, Pierre Nkurunziza, will become Burundi's next president when parliament chooses the next head of government on 19 August.
"The tendency in the municipal elections will be confirmed," said Willy Nindorera, a Burundi analyst. "The people recognise the FDD for having brought reforms into the army."
The FDD replaced armed struggle with representation in the country's military in 2003 when it became part of the transitional government.
Under Burundi's new constitution that was overwhelmingly endorsed in a February referendum, the National Assembly will be 60% Hutus and 40% Tutsis.
The Tutsis, who make up 15% of the country's population, will lose the dominant position they have enjoyed since independence from Belgium in 1962.