BAGHDAD, Iraq – Iraqis across ethnic, sectarian, and religious divides voted in droves yesterday in a high-stakes election that could determine the course of the country and the success or failure of the American effort to promote Western-style democracy in the Middle East.

In Baghdad, Mosul, and Basra, and in tiny hamlets along river valleys, in the mountainous Kurdish north, the marshy Shiite south, and the arid Sunni Arab west, voters sensed the day’s gravity and packed the polling places, dipping their fingers in purple ink after casting ballots for a full-time 275-seat legislature.

“May God protect Iraq and Iraqis,” voters in the Sunni city of Fallujah chanted as trays of rice and meat were carried into the election center, compliments of a local sheik with tribal ties to the insurgency.

Yesterday’s election, the third nationwide vote in 11 months, will decide the composition of the legislature that will form a four-year government, the country’s first permanent administration since the 2003 American-led invasion that toppled Saddam Hussein.

Its results will determine how much and how quickly Iraq will move toward a federal system with several semi-autonomous regions after decades under Saddam’s dictatorial Sunni-dominated central government, how much it will adopt Islamic principles after decades of secular rule, and whether it will move closer toward Shiite Muslim-led Iran to the east or pro-American Arab regimes to the west.

American officials hope the vote will stabilize the country and allay domestic fears that Iraq has turned into a political and military quagmire with no foreseeable end.

“There’s a lot of joy as far as I’m concerned in seeing the Iraqi people accomplish this major milestone in the march to democracy,” President Bush said at a White House meeting with Iraqi out-of-country voters. “I believe freedom is universal. I believe the Iraqi citizen cares just as much about freedom and living a free life as the American citizen does.”

In Iraq, Senator Biden, a Democrat of Delaware, said the American people are watching the election and post-election period closely, knowing that a harmonious and inclusive Iraqi government is a step toward bringing American troops home. He issued what he said was a challenge to Iraqi politicians to rise above sectarian tensions and petty rivalries which plagued the formation of an interim government after January’s vote and also surfaced later during the drafting of a national constitution.

“After the elections, [the American people] will be looking to see what’s next. Will the country come together, or will it fall apart?” Mr. Biden said after visiting a polling station in the southern city of Hillah.

The top American commander in Iraq said yesterday that voter turnout in the largely Sunni Anbar province “increased fairly substantially” over the October levels. General George W. Casey also said he expects the insurgency will “gradually reduce as the root causes of the insurgency are addressed.”

Even with yesterday’s balloting, however, General Casey predicted continued violence and political turmoil as Iraqis work to forge a new government. During the first six months of 2006, General Casey said, he expected “fairly divisive” fights over amending the Iraqi constitution and the issue of federalism for Iraq’s main principal ethnic groups.

While final results won’t be available for days, the election may well be remembered as one that cemented Iraq’s new political status quo: a big Shiite religious bloc with clerical backing is likely to grab the most seats; the Kurds with at least 20% of the votes and seats will maintain their grip on Kirkuk and on ministries in Baghdad; the great secular hope for America and Iraqi liberals, Ayad Allawi, is likely to again dash expectations by falling short in the popular vote, and the minority Sunnis, once they find having a parliamentary platform won’t mean they can simply boot out American troops, are likely to remain angry and resentful.

Election officials estimated that between 10 million and 11 million of Iraq’s 15.5 million registered voters turned out, equal to or more than the turnout during the October constitutional referendum.

With a strong Iraqi government security presence, violence was relatively low compared to the country’s daily litany of bloodshed. There were five known deaths caused by insurgent attacks. An attack on a polling site west of Kirkuk left two police officers dead after a 30-minute gunfight, a police official in the city said. A roadside bomb near Baqouba northeast of Baghdad killed one and injured four. A Tall Afar civilian was killed by a mortar shell, and additional mortar rounds fell on the capital and Mosul, causing several injuries, including to a 7-year-old girl in Baghdad’s Sadr City neighborhood. A school guard in Mosul was also killed in an insurgent attack yesterday.

Of the country’s 6,246 polling stations, 162 were closed yesterday for security reasons. In volatile Anbar province, 20 fewer voting centers were shut down yesterday than were in the October election.

Election officials reported minor irregularities, including ballot shortages and frustrated voters who couldn’t find their names in registration rolls.