There were no reports of widespread violence as voting got under way, although a shooting occurred in Baghdad's Sadr City district. According to Shiite lawmaker Ghufran al-Saidi, a military officer opened fire and injured two people after voters chanted slogans at a polling station.
But Iraq's military spokesman, Maj. Gen. Qassim al-Moussawi, told Al-Arabiya television that the shooting occurred after some people tried to carry mobile phones through security cordons. One person was killed and one injured, he said.
The reason for the conflicting accounts was not immediately clear.
In Tikrit, about 80 miles (130 kilometers) north of Baghdad, three mortar shells exploded near a polling station, but caused no casualties, said police, who spoke on condition of anonymity because they were not authorized to speak to media.
A bomb found near a Tikrit voting center was defused, police added.
Signs of the blanket security measures were everywhere. In the Baghdad neighborhood of Karradah, Iraqi police and army soldiers manned a series of checkpoints
- some only 200 yards (meters) apart. Stores were closed and the streets cleared of cars.
A group of U.S. soldiers patrolled on foot, but well away from polling centers. The U.S. military assisted in security preparations for the elections, but said troops would only be called in on election day if needed.
In the western city of Fallujah - once a center of the Sunni insurgency - police used their patrol cars to help some people get to voting stations.
More than 14,000 candidates, including about 3,900 women, are running for 440 seats on the influential councils in all of Iraq's provinces except for the autonomous Kurdish region in the north and the province that includes oil-rich Kirkuk, where ethnic groups were unable to reach a power-sharing formula.
Polls were to close at 5 p.m. (1400 GMT, 9 a.m. EST). Preliminary results are not expected before Tuesday.
Voters headed home waved their purple-tinted index fingers, which are dipped in ink to identify people who already cast ballots. The ink-stained fingers became an iconic image of Iraq's first post-Saddam Hussein elections four years ago.
Prime Minister Nouri al-Maliki, shadowed by a bodyguard, dipped his finger into an ink box after voting in the walled Green Zone enclave in Baghdad.
He appealed for a high turnout - which would help boost his government's attempts to use the election as a sign of progress.
"This gives a picture of trust in the government, the elections and the people's right to take part in this democratic process," he said.
Although violence is sharply down - and with pre-election attacks relatively limited
- authorities were unwilling to take any risks.
An election without major attacks or charges of irregularities would provide a critical boost for Iraqi authorities as the U.S. military hands over more security responsibilities. But serious bloodshed or voting chaos could steal momentum from supporters of a fast-paced withdrawal of U.S. combat troops next year.
The provincial councils have no direct sway in national affairs, but carry significant authority through their ability to negotiate local business deals, allocate funds and control some regional security operations.