Iraqis have voted for their first full-term government since the US-led invasion in 2003 amid tight security.
Voters have to dip their finger in ink to guard against multiple voting
A steady stream of people turned out to vote, report BBC journalists at polling stations across the country.
Several incidents of violence were reported soon after polls opened, but voting was not seriously disrupted.
A high turnout from Sunni Arabs, who boycotted the last election, is hoped for. President Jalal Talabani called on Iraqis to make it a day of celebration.
Some 15 million Iraqis are eligible to vote.
Initial indications suggest turnout had been very high with few irregularities, US ambassador Zalmay Khalilzad told the Associated Press.
Iraqis had to walk to polling stations as vehicles have been banned to prevent attacks on voters.
The BBC's Jon Leyne, at a polling station in a Baghdad school, said voting was very brisk there.
A US Bradley armoured fighting vehicle patrolled the street outside, and there was a heavy presence of mainly Iraqi police and soldiers in the polling station itself, he said.
About 150,000 Iraqi soldiers and police officers were on patrol across the country, backed up by US soldiers. Land borders and airports have been closed.
"Iraqis are living a historical moment today - that is the elections... we hope to live in stability and security in Iraq, in the north and in the south, east to west," Baghdad voter Shaab Ahmad told the BBC.
Election officials said some polling stations in Ramadi and the restive Anbar province, west of Baghdad, did not immediately open for security reasons. Most opened in the northern city of Mosul. Despite the stringent security measures, low-level violence was reported within minutes of polls opening:
- A huge blast was heard near the heavily-fortified Green Zone, home to the Iraqi government and a number of Western embassies. There were no reports of casualties
- Mortar fire was heard in a number of areas around Baghdad, with reports of at least two civilians wounded
- In Mosul, a hospital guard was killed when a bomb went off near a polling station, witnesses said
- A mortar round targeted a polling station in Saddam Hussein's home town of Tikrit
- On the eve of voting, bombs were uncovered and defused near a number of polling stations in Baghdad, Falluja and other cities, the US military said
Among the first people to cast their ballot was Mr Talabani, who voted in the northern city of Sulaimaniya.
"This is a good day and the Iraqi people bear the responsibility to vote for a better future. I hope that the Iraqi people will stay united. We hope that the people will vote to keep the constitution that was approved by the Iraqi people," Mr Talabani said.
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
Over 14 million eligible to vote
One third of candidates in each party must be women
Some 6,655 candidates, 307 parties and 19 coalitions registered for Thursday's ballot, electoral officials say.
Official results are not expected until later in the month.
It is the second time this year Iraqis have voted for a new government.
Turnout is expected to have been much larger than the vote in January, which was largely boycotted by the Sunni Muslim minority.
Sunnis were expected to actively participate this time, in a vote for a national assembly that will serve a full four-year term. The current government is Shia-dominated.
Even some insurgent groups called on people to vote, though al-Qaeda described the elections as the work of Satan.
The most senior British general in Iraq, Lt Gen Nick Houghton, told the BBC the elections give "growing confidence" that coalition forces can begin to withdraw in the "relatively near future, certainly during the first half of next year" if the conditions are right.