Other analysts said recent opinion polls indicate that many Iraqis viewed the election as one way to accelerate the U.S. withdrawal rather than as a vindication of U.S. policy. "They realize that the quickest way to get the United States out of Iraq is to create a new government," said Henri Barkey, a former State Department policy planning staff member now at Lehigh University. "Not to vote would mean a continuation of the status quo. So the election is not a vindication of U.S. policy."
Middle East analysts are most concerned about how the divide among the electorate yesterday could translate into trouble when Iraqis get down to forming a government and particularly writing a constitution.
_____More on Elections_____
Photo Gallery: The end of Iraq's Election Day brought indications of strong turnout, but also reports of at least 30 people killed.
Transcript: Pulitzer Prize-winning Washington Post foreign correspondent Anthony Shadid will discuss the elections and the latest news from Iraq.
Transcript: The Post's Jackie Spinner discussed the scene in Irbil, where elation at electing a new Kurdish parliament has Kurds partying in the streets.
Graphic: Voting Sites Attacked
Primer: What's Next For Iraq?
"We shouldn't get hysterical with hyperbole, we shouldn't have a 'mission accomplished' moment," said James Zogby, president of the Arab American Institute and an analyst with Zogby International, a New York-based polling firm. "Our polls show that the divisions are quite deep."
He compared Iraq's election to the 1860 U.S. election, which paved the way for the Civil War after Abraham Lincoln won -- and South Carolina seceded. "This election could exacerbate the divide," Zogby said. "You can't have 20 percent of the population feel disenfranchised."
Administration officials concede that the biggest problem will be bringing Sunni Muslims, who reportedly turned out in the smallest numbers, into the new government that will be formed over the next month and then into constitutional talks.
On ABC's "This Week," Rice said she had been "heartened" by pledges from "innumerable" leaders from Iraq's disparate religious and ethnic groups that they expect the 20 percent Sunni minority, which once dominated Iraqi politics, to be incorporated into the process even if they didn't vote.
Appearing on four Sunday talk shows, Rice told ABC that the significant turnout in defiance of the violence and threats to anyone who voted showed that democratic principles "have no boundaries; they're not Western values. These are universal values."
The apparently healthy turnout in Iraq's election won praise from some of the toughest critics of the U.S. intervention in Iraq. France, which led opposition to a U.N. resolution approving the use of force to topple Saddam Hussein in 2003, called Iraqis "courageous" and said the vote was "necessary," despite earlier calls to delay it.
"This is a great victory, if this process succeeds, first and foremost for the Iraqis who together felt sufficiently courageous despite the hardships, despite the violence, to go and vote," said French government spokesman Jean-Francois Cope.
Javier Solana, the European Union's foreign policy chief, congratulated Iraqis and backed off from a warning last week that the vote could become "a disaster" if the Sunni minority emerged without representation.
"The elections represent an important step forward for Iraq. Despite the many difficulties that lie ahead, the elections mark progress towards a transition to a democratic, free and peaceful Iraq," he said in a statement.
To strengthen relations at this strategic juncture, Rice leaves Thursday on her first trip as secretary of state for talks in Europe and the Middle East.