Iraqis have voted in large numbers for their first full-term government since the US-led invasion in 2003.
Voters had to dip their finger in ink to guard against multiple voting
Voting was extended by an hour in some areas because of the high turnout, Iraq's election commission said.
Sunni Arabs, who boycotted the last election in January, appear to have participated in large numbers, even in insurgent strongholds.
Despite tight security, several incidents of violence were reported, but voting was not seriously disrupted.
About 150,000 Iraqi soldiers and police officers were on patrol across the country, backed up by US soldiers. Borders and airports were closed.
Turnout is reported to have quickened throughout the day, with people queuing to cast their ballots.
IRAQ ELECTION FACTS
275-seat National Assembly will have four-year term
18 provinces are taken as separate constituencies
230 seats allocated according to size of population
45 seats distributed to parties whose ethnic, religious or political support is spread over more than one province
Some 15 million eligible to vote
One third of candidates in each party must be women
That was the case even in the predominantly Sunni cities of Falluja and Ramadi, hotbeds of insurgent activity. At one stage, an election official in Falluja said that so many people were voting, they had run out of ballot papers.
Sunni nationalist insurgent groups had urged people to vote, in order to prevent the election of a government completely dominated by Shias and Kurds.
However, the al-Qaeda in Iraq group denounced the election as the work of Satan and threatened attacks.
It is believed to have been behind an explosion in Baghdad's fortified Green Zone, which houses government buildings, shortly after the polls opened. Two civilians and a US marine were slightly injured.
'Day of victory'
Some 15 million Iraqis were eligible to vote.
Most had to walk to polling stations as movement of vehicles was banned to prevent car bomb attacks.
"It's a day of victory, a day of independence and freedom," said 60-year-old Shia Muslim Mohammed Ahmed al-Bayati as he voted in Baghdad.
Teacher Khalid Fawaz in Falluja said he was voting "so that the Sunnis are no longer marginalised".
Crowds turned out in Basra, the largest city in the Shia-dominated south, as well as the holy city of Najaf, dancing and chanting support for the alliance of religious Shia parties which is expected to win the largest number of seats.
BBC World Affairs Editor John Simpson in Baghdad says the voters he spoke to believe the election will help to bring about a strong, effective government of the kind Iraqis are desperate for.
He says people also think it will bring Sunnis into government in some strength, and that it will get rid of the Americans and British, whose military presence is widely disliked.
But he adds that Iraqi politicians are well aware that this positive feeling will evaporate if it takes them as long to form a coalition government as it did after the January election.
The new national assembly will replace the transitional government elected in January, and will serve a full four-year term.
Some 6,655 candidates, 307 parties and 19 coalitions registered for the ballot, electoral officials say.
A spokesman for the Independent Electoral Commission, Fareed Ayar, said results would be announced "within two weeks".