US President Barack Obama praised provincial elections in Iraq on Saturday as an "important step forward" for the future of the country.
Security for the country's first ballot since 2005 was extremely tight with police and the military deployed in force. The election was peaceful.
Around 14,400 candidates were seeking 440 council seats in 14 of the 18 provinces. Provincial councils select regional governors.
Three Kurdish provinces will vote separately and the election was indefinitely postponed in the northern city of Kirkuk.
Almost 15 million people were registered to vote. Early results will be issued on Tuesday but the final outcome will take several weeks.
Voting was extended by one hour due to a strong turnout.
Mr Obama opposed the Iraq war. In a statement, he praised technical assistance by the United Nations and other organisations to the electoral commission, which he said "performed professionally under difficult circumstances".
He said "it's important that the councils get seated, select new governors and begin work on behalf of the Iraqi people who elected them."
Prime minister Nuri al-Maliki said the peaceful election was "a victory for all Iraqis".
A previous election took place in 2005 amid a Sunni insurgency and was followed by a surge in sectarian slaughter between Sunnis and Shi'ite Muslims. Fewer than 2% voted in that election.
US-led forces invaded Iraq in 2003 and ousted president Saddam Hussein.