A series of attacks has killed at least 30 people - mainly in Baghdad - as voters take part in Iraq's first multi-party elections for 50 years.
Queues outside polling stations have been targeted by bombers
Correspondents said there were crowds and smiles in the south and north as voters made their choices for a 275-member national assembly.
But few voters turned out in Sunni areas around the capital, reports said.
Iraq's electoral commission says up to 72% of voters cast ballots but the UN offered a more cautious assessment.
More than 100 parties and coalitions are competing for seats in the transitional assembly, which will draft a new Iraqi constitution ahead of planned elections for a full-term parliament.
Polls officially closed at 1400 GMT, but officials said anyone still in line would be allowed to vote.
Outbreaks of violence
Some parties had called on voters to boycott Sunday's election and accused militant leader Abu Musab al-Zarqawi vowed to try to disrupt the process.
Authorities imposed an unprecedented series of security measures - including a shoot-on-sight policy during curfews, sealed borders, a ban on cars and travel restrictions within Iraq - in a bid to forestall violence.
But a spate of attacks hit Baghdad and surrounding areas in the hours after polls opened at 0700 (0400 GMT).
- At least three people died in an explosion on a bus reportedly carrying Sunni Arabs to a polling station south of Baghdad
- At least six people died when a bomber with explosives strapped to his body blew himself up outside a polling station in eastern Baghdad
- In western Baghdad, a suicide bomber killed at least four others and injured at least six people outside a polling station, and four policemen were reportedly killed in separate suicide attacks on polling stations
- In the capital's Sadr City district, at least four people died and seven were wounded when a mortar struck a polling station, and four other people were reported to have died in other attacks in or near the capital
- Explosions were also heard in Basra, Mosul and Baquba - where fighting is reported to have broken out in the south of the city
- One guard died in an apparent assassination attempt on the interim justice minister, who was untouched.
Despite the attacks in Baghdad, voting at polling stations in the country's mostly Shia Muslim south and Kurdish north was said to be brisk.
Iraq's electoral commission held a news conference 90 minutes before polls closed to say turnout was estimated at 72%, with 90% or more in some Shia areas.
But electoral official Adil al-Lami did not say how these figures had been reached.
Earlier, the top UN electoral adviser Carlos Valenzuela offered a much more cautious assessment, saying turnout appeared to be high in many areas, but that it was too early to know for sure.
Some voters at polling stations described the day as "the most important in their lives".
The BBC's Peter Grant in the small town of Abu al-Khasib, just south of Basra, said one man arrived at the polling station clutching a written speech about his joy at voting.
In Basra, polling stations had to open some minutes early due to queues forming.
The BBC's Jim Muir in the mostly Kurdish city of Irbil says voting has now dwindled after a large turnout before lunch.
He says voters there are eager to secure as big a bloc of seats as possible in the transitional national assembly in Baghdad, so that the Kurdish desire for autonomy will be taken into account as the new constitution is drafted.
Election officials have also reported high turnouts in Shia pockets of Sunni-dominated central Iraq.
But reports from central Sunni cities, such as Falluja, Samarra and Ramadi, say few polling stations are open, and there is at best a trickle of voters.
A number of factors may lie behind residents' decision to stay away from the polls, say correspondents.
Insurgent threats of violence may have deterred some, but others may be obeying boycotts of the elections called by some Sunni political parties. Others may not want to legitimise an election they believe is offering false hope.
You can watch John Simpson's Panorama programme on the state of Iraq on BBC One on Sunday 30 January at 2215 GMT and on BBC World television on Saturday 5 February at 0810, 1210 and 2210 GMT.