BAGHDAD — Bomb attacks and mortar fire failed to prevent Iraqis voting in the first nationwide elections since the last U.S. troops left more than a year ago.

The provincial elections will measure political parties' strength before a parliamentary election in 2014 to chose a new government in a country deeply divided along sectarian lines.

A dozen small bombs exploded and mortar rounds landed near polling centers in cities north and south of the capital. Three voters and a policeman were injured by mortars in Latifiya, south of Baghdad, police said.

The violence on Saturday was relatively low key for a country where a local al-Qaida wing and other Sunni Islamists have stepped up their efforts to undermine the Shi'ite Muslim-led government and stoke confrontation along religious and ethnic divides.

Preliminary results were not due for several days, but election authorities said 50 percent of eligible voters — more than 6.4 million — took part in Saturday's poll, a similar rate to the last vote for provincial councils in 2009.

After polls closed, a local official in Baquba, about 40 miles northeast of Baghdad, said disgruntled voters who were unable to find their names on the electoral lists burned four boxes of ballots at one polling station.

Since U.S. troops left in December 2011, Iraqi politics has been paralyzed by infighting over power-sharing agreements, with Maliki's rivals accusing the Shi'ite premier of consolidating power at the expense of Sunni and Kurdish partners.

For Maliki, a strong showing by his Shi'ite State of Law alliance may consolidate his plans to abandon the unwieldy power-sharing deal to form a majority government.

Sunni rivals, deeply divided over how to work with his government, will look to chip away at Maliki's hold over provincial councils.

Many voters appeared caught between hope for improvement, apathy and resignation about how much would change after the election of nearly 450 provincial council members who have the power to elect state governors.

"People are not patient, they were not ready for how quickly we came to democracy," said Ahmed Abdel Hameed, voting in Baghdad a decade after U.S. troops crossed the border in an invasion that ousted President Saddam Hussein.

"They thought everything would change in one election. We still need time, maybe we need three or four more elections," he said.

 Most Iraqis are frustrated with insecurity, unemployment, corruption and the lack of basic services 10 years after the invasion that was followed by sectarian bloodshed that killed tens of thousands of people.

Violence has eased since a peak in 2006-2007 but insurgents are still capable of inflicting major damage.

Attacks on one Sunni and one Shi'ite mosque on Friday killed at least eight people. A suicide bomber killed 32 at a cafe in a mostly Sunni neighborhood in Baghdad a day before.

"Overall the elections are likely to see Iraq stumble further along the trajectory on which it has already been headed for some time: to stratified, sectarian politics," Eurasia Group analyst Crispin Hawes wrote in a report.

Voting was postponed in two mostly Sunni provinces because local officials warned they could not provide security there, a decision that prompted Washington to call on the government to ensure it did not alienate Sunni voters.

Since December, tens of thousands of Sunnis have taken to the streets each week to demonstrate against what they say is the marginalization of their minority, sidelined by the majority Shi'ite leadership and discriminated against by Iraqi security forces and tough anti-terrorism laws.

Election authorities said voting that was suspended in Anbar and Nineweh provinces may go ahead in a month.

"Suspending elections was the coup de grace for the demonstrations. We've lost everything," said Maitham Jalal, a college student in Anbar province. "Elections are a legitimate right which was taken away by the government without any fear."