Insurgents seeking to wreck the vote struck polling stations with a string of suicide bombings and mortar volleys, killing at least 44 people, including nine attackers.
In Khadimiya, a mixed neighborhood in Baghdad, people were streaming in, despite explosions and gunfire nearby, reports CBS News Correspondent Charlie D'Agata.
Standing on the roof of the police station in Askan, in the Sunni Muslim-dominated "triangle of death" south of Baghdad, - Sunni and Shia, men and women, young and old, some with their children, and many smiling and shaking hands as they waited their turn to enter one of two classrooms to cast their ballots.
The since the fall of Baghdad and the subsequent capture of Saddam Hussein, reports CBS News Anchor Dan Rather.
In other developments:
Officials said turnout among Iraq's 14 million eligible voters appeared higher than the 57 percent that had been predicted. No preliminary results were expected before Monday at the earliest, and final results will not be known for seven to 10 days, the election commission said.
Polls were largely deserted all day in many cities of the Sunni Triangle north and west of the capital, particularly Fallujah, Ramadi and Beiji.
In Baghdad's mainly Sunni Arab area of Azamiyah, the neighborhood's four polling centers did not open at all, residents said.
A low Sunni turnout could undermine the new government that will emerge from the vote and worsen tensions among the country's ethnic, religious and cultural groups.
Prominent Iraqi Sunni politician Adnan Pachachi, who in recent months had called for the vote to be postponed because of violence, told a cable news channel he was "relieved" and "encouraged" by a turnout he said was better than expected, even in Fallujah and Mosul.
Shiite Muslims, estimated at 60 percent of Iraq's 26 million people, were expected to vote in large numbers, encouraged by clerics who hope their community will gain power after generations of oppression by the Sunni minority.
After a slow start, voting appeared heavy in Shiite and mixed Shiite-Sunni neighborhoods in Baghdad but low in some heavily Sunni areas. Sunnis in mixed areas may have voted in greater numbers there because pressure to boycott was less intense — and chances of retaliation lower because they would not stand out at the polls. There are few ways by sight to distinguish Sunni and Shiite Arabs.
The election will create a 275-member National Assembly and 18 provincial legislatures. The assembly will draw up the country's permanent constitution and will select a president and two deputy presidents, who in turn will name a new prime minister and Cabinet to serve for 11 months until new elections are held.
It is during this 11 months that the brokering begins and the conflicts are ironed out between the different sectors of Iraqi society, says CBS News Foreign Affairs analyst Pamela Falk.
Any expectations that Iraq's democracy will arise as fast as Saddam Hussein's government fell, are unrealistic, says Patrick Basham, senior fellow at the Cato Institute.
"Right now, Iraqis really don't understand or appreciate the kind of liberal democracy, the kind of freedoms we take for granted," Basham said. "It is going to take a long time for there to be that kind of change. I think it appears that we're going to go forward now with at least, on paper, a democratic system. But the key question is, can in the coming months and years, the Iraqi people themselves make this system work because they actually believe in it and wish to sustain it."
Guerrilla attacks began within two hours of the balloting's start Sunday morning. All but one of the day's nine suicide attacks came in Baghdad, mostly against polling sites, using bombers on foot with explosives strapped to their bodies since private cars were banned from the streets.
In one of the deadliest attacks of the day, a bomber got onto a minibus carrying voters to the polls near Hillah, south of Baghdad, and detonated his explosives, killing himself and at least four other people, the Polish military said.
A deadly mortar volleys hit Baghdad's Shiite neighborhood of Sadr City and others struck voters at several sites in Balad, and Kirkuk in the north and Mahawil south of the capital. Across the country, at least 35 people and nine suicide bombers were killed.
The group al Qaeda in Iraq, led by Abu Musab al-Zarqawi, claimed responsibility for election-day attacks in a Web statement, although the claim could not be verified.
Concern over violence was rife as voters entered polling stations under loops of razor wire and the watchful eye of rooftop sharpshooters. About 300,000 Iraqi and American troops were on the streets and on standby to protect voters
In Ramadi, U.S. troops tried to coax voters with loudspeakers, preaching the importance of every ballot. The governor of the mostly Sunni province of Salaheddin, Hamad Hmoud Shagti, went on the radio to lobby for a higher turnout.
Several hundred people turned out to vote in eastern districts of the heavily Sunni city of Mosul — Iraq's third largest city and a center for insurgent violence in past months. But in western parts of Mosul, clashes erupted between guerrillas and Iraqi soldiers.
A ticket endorsed by the country's leading Shiite cleric, Grand Ayatollah Ali al-Sistani, is expected to fare best among the 111 candidate lists. However, no faction is expected to win an outright majority, meaning possibly weeks of political deal-making before a new prime minister is chosen.