The United States president has praised Iraqis for having the courage to turn out to vote in the country's elections, despite insurgent attacks that killed at least 38 people.
Barack Obama hailed the election as an important milestone in Iraq's history, but acknowledged it was one stage in a long process.
US Defence Secretary Robert Gates praised the Iraqi security forces for preventing al Qaeda staging more deadly attacks in the second parliamentary election since the 2003 invasion.
Despite bomb and mortar attacks, there were long queues at polling stations in Baghdad and in Sunni towns.
Officials say turnout was 62% - higher than in last year's provincial ballot - despite the attacks.
A strong turnout was reported in Sunni areas of the country, where many people in 2005 decided not to vote.
Two buildings were destroyed in the capital and dozens of mortars were fired across Baghdad and elsewhere.
An immense security operation was mounted, involving more than 500,000 Iraqi security personnel.
The border with Iran was closed, thousands of troops were deployed, and vehicles were banned from roads.
On Friday, al Qaeda threatened to kill voters, days after a series of suicide attacks and bombings killed dozens of Iraqis.
Prime Minister Nuri al-Maliki said the attacks were "only noise to impress voters but Iraqis are a people who love challenges and you will see that this will not damage their morale".
Mr Maliki cast his vote in Baghdad's fortified Green Zone which houses the parliament and the United States and British embassies. The zone was the target of several mortar hits.
About 6200 candidates competed for 325 seats. About 19 million Iraqis were eligible to vote.
Election officials say it could take several days for preliminary results to be released.