Election officials began tallying votes on Sunday from Iraq's first elections since US troops departed, a contest that served as a key test of its stability amid a spike in violence.

Attacks killed three people on election day, a fraction of those who died in a wave of violence preceding the polls on Saturday, which seemed generally well-organised.

Turnout for the provincial vote was about 51 percent, according to officials from Iraq's Independent High Electoral Commission.

IHEC board member Gaata al-Zobaie said ballot boxes and tallies from polling stations were being sent to Baghdad, and they would be entered in computers to tabulate the results.

But the credibility of the elections came into question, as 14 candidates died in attacks ahead of the polls and with a third of Iraq's provinces -- all of them mainly Sunni Arab or Kurdish -- not voting due to security concerns and political disputes.

The vote for provincial councils, responsible for naming governors who lead local reconstruction, administration and finances, is seen as a key gauge of Prime Minister Nuri al-Maliki's popularity ahead of a general election next year.

Every Iraqi who votes "is saying to the enemies of the political process that we are not going back," Maliki said on state television after casting his ballot at the Rasheed Hotel in Baghdad's heavily-fortified Green Zone.

Security was tight on Saturday, with voters searched before entering polling stations and numerous new checkpoints set up by soldiers and police in Baghdad.

For most of the day, only approved vehicles were allowed on the streets, which were largely deserted except for security forces and groups of children who took the opportunity to play football.

Despite heightened security in Baghdad and elsewhere, militants were still able to carry out attacks, although the death toll was much lower than the previous six days, when an average of 20 people were killed daily.

Nine mortar rounds, four bombings and five stun grenades, all outside Baghdad, killed three people and wounded two, officials said.

And gunmen dressed in police uniforms entered a polling station near Baquba, north of Baghdad, burned ballot boxes, then escaped.

The elections, which came a decade after US-led forces ousted now-executed dictator Saddam Hussein, were the first since parliamentary polls in March 2010, and also the first time Iraqi forces secured elections without support from American or other international forces since 2003.

US troops withdrew in December 2011.

An estimated 13.8 million Iraqis were eligible to vote for more than 8,000 candidates, with 378 seats being contested.

Major issues affecting voters such as poor public services and rampant corruption were largely ignored during the campaign.

The United States and United Nations both called in statements for elections in Anbar and Nineveh provinces, which the Iraqi government said were postponed due to security concerns, to be held as soon as possible.

"Security concerns should not prevent all Iraqi citizens from expressing themselves democratically," the US statement said.