US President Barack Obama has congratulated Iraqis for holding a largely peaceful vote for provincial councils across the country.
He called the elections "an important step forward" for Iraqi self-determination. PM Nouri Maliki hailed them as "a victory for all the Iraqis".
There was a strong turn-out in Sunni areas, which 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.
"I congratulate the people of Iraq on holding significant provincial elections today," Mr Obama said in a statement.
"This important step forward should continue the process of Iraqis taking responsibility for their future."
Mr Obama urged the newly elected councils to "get seated, select new governors, and begin work on behalf of the Iraqi people who elected them".
Earlier, Mr Maliki said this was "a day of happiness for all the Iraqi people and for all those who love Iraq".
The BBC's Andrew North in Baghdad says that while Iraq is not yet at peace, the election is a promising sign that it is on the way there.
Thousands of soldiers and police were deployed around polling stations.
This time we won't let those people who have let us down in the past reach power again
Lubna Naji Medical student
The elections were held in 14 of the country's 18 provinces, with more than 14,000 candidates competing for just 440 seats.
There was no voting in the three provinces of the semi-autonomous Kurdish region of the north and the ballot was 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.
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
Voters had to pass through stringent security checks to reach the polling stations.
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 monitored the vote, as well as thousands of local observers from the various political parties.
The turnout was reported to be brisk across the country - including Sunni areas.
Jim Muir takes a look inside an Iraqi polling station
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.
Fewer than 2% voted in the 2005 election, with the result that Shia and Kurdish parties took control of parliament.
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.
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