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.
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.
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.
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. BBC