Iraq's election commission kept polling places open an extra hour because of the high turnout. They had been scheduled to close at 9 a.m. EST.
Several explosions rocked Baghdad as the polls opened, including a large one near the heavily fortified Green Zone that slightly injured two civilians and a U.S. Marine, the U.S. military said. An Islamic insurgent group, the Victorious Sect Army, posted a claim of responsibility on a Web site within hours. The claim was not verified.
But violence overall was light and did not appear to discourage Iraqis, some of whom turned out wrapped in their country's flag on a bright, sunny day and afterward displayed a purple ink-stained index finger — a mark to guard against multiple voting.
"The sense I got from speaking to people here in Baghdad was that this is an historic day here and Iraqis are anxious to stand on their own and govern themselves without occupation," reports CBS News correspondent Lara Logan. "Even in hostile Sunni areas that shunned the last election, turnout already appears to be strong."
In other developments:
"There's going to be a real election here and I think there's going to be a significant turnout. That's a very important first step," Biden said on CBS News' The Early Show.
A civilian was killed when a mortar shell exploded near a polling station in the northern city of Tal Afar, and a bomb killed a hospital guard near a voting site in Mosul.
The turnout in Anbar province, where the insurgency has been so deadly, was steady all day long, reports CBS News correspondent Cami McCormick. One polling station ran out of ballots at midday. Voters often walked more than a mile in some cases to get to polling places, because civilian cars had been banned from the roads. Some carried Iraqi flags. Some sang and chanted.
While Iraqis didn't openly present ink-stained fingers, they were quick to do so if U.S. soldiers passed through their villages. Local sheiks provided security at most of the polling places. In some cases, they blocked off their villages to outsiders so that the voting would be peaceful.
Sunnis appeared to be turning out in large numbers — even in insurgent bastions such as Ramadi and Haqlaniyah — in an effort to curb the power of Shiite clerical parties who now control the government.
"I came here and voted in order to prove that Sunnis are not a minority in this country," said lawyer Yahya Abdul-Jalil in Ramadi. "We lost a lot during the last elections, but this time we will take our normal and key role in leading this country."
And 28-year-old college student Yassin Mohammed Samarra said he voted so that "no particular (religious) sect controls the country."
Shiite parties had urged their followers to turn out in large numbers, too. The country's leading Shiite cleric, Grand Ayatollah Ali al-Sistani, told Shiites to support candidates who defend their principles — a veiled warning against turning toward secular political movements.
Turnout was also brisk in the northern cities of Mosul and Kirkuk, especially in Kurdish districts.
"This is the day to get our revenge from Saddam," said Kurdish voter Chiman Saleh, a Kirkuk housewife who said two of her brothers were killed by the ousted regime.
"They do want to vote. They want to choose their leader. The part they've never done before is then they have to make the serious compromises that are necessary for democracy," Biden told Early Show co-anchor Harry Smith. "You have the religiously-bent Shia in the south that want to set up an Islamic state. You have the secular folks in the Sunni area, and some in the north, who don't want a religious state. They're going to have to make some serious compromises."
President Jalal Talabani, a Kurd, highlighted a key looming fight — possible amendments to the constitution — as he voted in the northern city of Sulaimaniyah.
"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," he said.
An alliance of Shiite religious parties, which dominate the current government, was expected to win the largest number of seats — but not enough to form a new administration without a coalition with rival groups. That could set the stage for lengthy and possibly bitter negotiations to produce a government.
Up to 15 million Iraqis were electing 275 members of the first full-term parliament since Saddam Hussein's ouster from among 7,655 candidates running on 996 tickets, representing Shiite, Sunni, Kurdish, Turkomen and sectarian interests across a wide political spectrum. Iraqis do not vote for individual candidates, but instead for lists — or tickets — that compete for the seats in each of the 18 provinces.
Some preliminary returns were expected late Thursday, but final returns could take days, if not weeks.
Election of the new parliament, which will serve a four-year term, marks the final step in the U.S. blueprint for democracy. The process included the transfer of sovereignty last year, selection of an interim parliament Jan. 30, and ratification of the constitution in October. The new parliament will name a government, including a new prime minister.