Preliminary results are not expected for several days
The voter turnout in Iraq's general elections was 62%, officials said, despite attacks that killed 38 people.
Preliminary results are not expected for several days but the turnout figure is down from the 75% who voted in the 2005 general elections.
Prime Minister Nouri Maliki's State of Law Coalition is widely expected to win the most seats.
But it is unlikely one party will form a government alone and there may be months of negotiations on a coalition.
IRAQI GENERAL ELECTION
Voting to elect 325-member parliament.
About 19 million eligible voters out of 28 million
Around 6,200 candidates from 86 factions competing
200,000 security personnel on duty in Baghdad
Key issues: Security, services and disqualification of alleged Baathists
Previous votes: Jan 2005 (transitional national assembly), Oct 2005 (constitution), Dec 2005 first post-invasion parliament, Feb 2009 (local elections)
Officials from the Independent High Electoral Commission estimated the turnout in Sunday's elections was 62% of the 19 million eligible voters.
The final official results will not be declared until the end of March, though preliminary results are expected in two or three days.
Mr Maliki's State of Law Coalition said it had done well, especially in Baghdad and in the Shia south of Iraq.
Unnamed Iraqi officials told the news agency AFP that he was leading in nine of Iraq's 18 provinces.
Mr Maliki faces competition from the Shia-dominated Iraq National Alliance and the secular coalition of former Prime Minister Iyad Allawi.
An official with Mr Allawi's Iraqiya alliance said the bloc was leading in the northern and western provinces.
Election officials gave further breakdowns of the turnout by region.
FROM GLOBAL VOICES
We are just tired from living in horror, we don't want to lose more people we love, this war was bloody and I just want it to end and be a bad memory in my life. I wonder if my relatives abroad will come back... Iraqis want their lives back
I can't wait till the day I'll wake up and open the curtains in my room and see life in my neighborhood again instead of a ghost city, I can't wait till the day that we'll remove the wood we placed over the windows...
I want to hear good news about rebuilding my country... not how many people who were killed.
is an 18-year-old Iraqi blogger from the city of Mosul, who voted for the first time
Voter turnout was reported to be 61% in the mainly-Sunni province of Anbar, which sprawls from west of Baghdad to the borders with Syria, Jordan and Saudi Arabia.
In the northern Kurdish-controlled autonomous area of Dohuk the turnout was 80%, news agency AFP reported.
There had been fears that Sunnis might stay away, amid feelings of widespread alienation from the political process after a widespread boycott of the 2005 elections.
Some 500 candidates, mostly Sunnis, were banned from running because of their alleged connections to the banned Baath party of former leader Saddam Hussein.
Despite the attacks in Baghdad and other cities including Mosul, Fallujah, Baquba and elsewhere, the election has been hailed as a "milestone" in Iraq's history.
Insurgents had threatened to disrupt the elections, but there were no large-scale suicide bombings as many had feared.
The most deadly strike was on an apartment block in Baghdad which collapsed, killing 25 people.
"Today's voting makes it clear that the future of Iraq belongs to the people of Iraq," Mr Obama said.