Prime Minister Nouri Maliki casts his vote
Iraqi Prime Minister Nouri Maliki has hailed a largely peaceful vote for new provincial councils across the country as a victory for all Iraqis.
Voting was extended by one hour due to a strong turnout, including among Sunni Muslims who boycotted the last polls.
The first nationwide vote in four years is seen as a test of stability before a general election due later this year.
US President Barack Obama hailed the poll as an "important step forward" for Iraqi self-determination.
"I congratulate the people of Iraq on holding significant provincial elections today," he said in a statement.
Thousands of soldiers and police were deployed around polling stations.
The election is also being seen as a quasi-referendum on the leadership of Mr Maliki.
"This is a victory for all the Iraqis," he said, after casting his vote in Baghdad's highly-protected Green Zone.
He said a high turnout would be an indicator of "the Iraqi people's trust in their government and in the elections" and "proof that the Iraqi people are now living in real security".
A peaceful vote could also set the stage for further coalition troop withdrawals, says the BBC's Jim Muir in Baghdad.
Up to 15 million Iraqis are eligible to cast votes.
The elections are being held in 14 of the country's 18 provinces, with more than 14,000 candidates competing for just 440 seats.
There is no voting in the three provinces of the semi-autonomous Kurdish region of the north and the ballot has been postponed in oil-rich Kirkuk province.
Iraq's provincial councils are responsible for nominating the governors who lead the administration and oversee finance and reconstruction projects.
While the recent level of violence around Iraq is significantly lower than in past years, a major security operation took place across the country.
Iraq's international borders were shut, traffic bans were put in place across Baghdad and major cities, and curfews introduced.
Hundreds of women, including teachers and civic workers, were also recruited to help search women voters after a rise in female suicide bombers last year, according to the Associated Press.
Voters had to pass through stringent security checks to reach the polling stations, which were mostly set up in schools, our correspondent says.
2003: US appoints Governing Council
2004: Governing Council elects interim government
Aug 2004: National conference elects interim national assembly
Jan 2005: First general elections for transitional national assembly and provincial councils - Sunnis boycott vote
Dec 2005: General elections for first full-term government and parliament
Jan 2009: Elections for provincial councils - key test of security gains
Late 2009: General elections due
Despite warnings from Iraqi and US military commanders that al-Qaeda posed a threat to the elections, there were relatively few incidents reported.
As voting got under way, several mortar rounds landed near polling stations in Tikrit, hometown of late ruler Saddam Hussein, but no casualties were reported.
Associated Press news agency reported a shooting incident at a polling station in Baghdad, but it was unclear if one man had been killed or two injured.
There were also reports that a number of people were not listed on voter rolls, preventing them from casting ballots.
Hundreds of international observers are monitoring the vote, as well as thousands of local observers from the various political parties.
After a slow start to voting, the pace picked up and there was a holiday atmosphere among voters walking to the polling stations, our correspondent says.
"People here are so excited by the feeling that their vote can make a difference," Lubna Naji, a Baghdad medical student, told the BBC News website.
She added that people knew better who to vote for than in 2005: "This time we know who cares for Iraq and its people and who only cares for their own interests and benefit.
"This time we won't let those people who have let us down in the past reach power again."
The turnout was reported to be brisk even in Sunni areas.
The head of the Iraqi electoral commission in Anbar province - a centre of the Sunni resistance to the US occupation - said he was expecting a 60% turnout.
Jim Muir takes a look inside an Iraqi polling station
Fewer than 2% voted in the 2005 election, with the result that Shia and Kurdish parties took control of parliament.
Some Sunnis, like Khaled al-Azemi, said the boycott last time had been a mistake.
"We lost a lot because we didn't vote and we saw the result - sectarian violence" he told the BBC.
"That's why we want to vote now to avoid the mistakes of the past."
The drawing of alienated Sunnis back into the political arena is one of the big changes these elections will crystallise, the BBC's Jim Muir reports from Baghdad.
On the Shia side, the results will also be closely watched amid signs that many voters intend to turn away from the big religious factions and towards nationalist or secular ones.