The high turnout on Thursday's polls prompted Iraq's election commission to extend voting by an additional hour around the country.
Adel al-Lami, the director-general of the Independent Electoral Commission, said: "We have issued an order to all centres in Iraq to extend the vote by one hour."
With voters lining up in large numbers, polling stations stayed open until 6pm (1500GMT). As voting ended, celebratory gunfire rang out in Baghdad, as much in jubilation as it was in relief for the day having passed off in relative peace.
The decision to extend the voting hours was the clearest indication that there was a large turnout at the country's more than 33,000 polling stations.
Hussein Hendawi, the electoral commissioner, said that turnout could have exceeded 10 million voters, or about 67%, well in excess of the 58% recorded on 10 January when Iraqis voted to elect an interim parliament.
Security was tight and the day
passed off in relative peace
In Saddam Hussein's home province around Tikrit, where few voted in January, the provisional turnout was 83%, an official in the local electoral commission said.
In preliminary estimates of turnout, the electoral commission said 80% of the electorate had voted in Salaheddin, 70% in the Shia town of Hilla and Najaf and 60% in Nasiriyah, further south.
Having boycotted the January polls, Sunnis appeared determined to make their voice heard.
In Falluja – the Sunni-dominated town and a hotbed of armed opposition to US-led forces - so great was the turnout compared with the previous vote that polling stations ran out of ballot papers during the day, causing long queues to form.
Entire families walked through the town's car-free streets while children enjoyed their holiday playing football.
The scene was in stark contrast to empty streets last January when the war-ravaged town boycotted elections for the transitional assembly.
By casting their ballots, Iraqis chose to ignore the explosions and violence reported during the day.
Two people were killed and three wounded in bomb and mortar attacks on polling stations at Mosul and Tal Afar in the north.
A dawn mortar blast claimed by a Sunni Islamist group wounded three people, including a US Marine, in Baghdad's Green Zone government and diplomatic compound, the US embassy said.
General calm imposed by a three-day traffic ban, sealed borders and heavy security was also broken by mortars in Samarra and nearby Tikrit. Another explosion rocked Ramadi.
The peaceful conduct of the polls and the high turnout warmed many hearts.
The United States hailed the elections as historic.
Scott McClellan, the White House spokesman, said: "This is a historic day for the Iraqi people, the Middle East and the world, a historic day for the advance of freedom."
"This is a historic day for the Iraqi people, the Middle East and the world, a historic day for the advance of freedom"
White House spokesman
Compliments poured in as well for the Iraqis from the United Nations and the British government.
There are no reliable opinion polls; but observers expect the United Iraqi Alliance (UIA), a grouping of conservative Shia Muslim parties within the current coalition government, to win the most votes.
Its share is expected to fall, however, from the 48% it won in January to perhaps about 40%.
The Kurds, the second-biggest bloc in parliament, are predicted to win about 25% of the vote, and will be pushed hard for second place by Iyad Allawi, a former interim prime minister, whose broad coalition took 14% in January but is expected to make ground.