Iraqis voted in force on Saturday on a draft constitution that turns another page on the ousted regime of Saddam Hussein amid a general calm that contrasted with violence during January's general election.
Insurgents nonetheless evaded a massive security clampdown to kidnap 10 poll workers and kill six other people.
Some 15.5 million Iraqis had a chance to vote on the charter, which lays out a democratic framework for a new Iraq but has sharply divided the country on ethnic lines and was drafted only after weeks of tortuous negotiations.
The charter requires a simple majority to be approved, but would be rejected if two-thirds of the votes in at least three of Iraq's 18 provinces say "no."
Results should be known within three days, chief electoral official Adil al-Lami said.
"But if people have serious complaints, of course we will check to see if they are justified. That would delay a final declaration," he said.
Celebratory gunfire broke out in several Baghdad neighbourhoods after polls closed, and senior electoral official Abdel Hindawi said that according to a preliminary estimate, more than 61 percent of registered Iraqis cast ballots.
In Washington, US President George W. Bush hailed the referendum as "a critical step forward" in war-torn Iraq's move towards democracy, whether or not the charter passed.
"By casting their ballots, the Iraqi people deal a severe blow to the terrorists and send a clear message to the world: Iraqis will decide the future of their country through peaceful elections, not violent insurgency," he said.
Kurdish President Jalal Talabani had said after casting his ballot inside Baghdad's heavily-protected Green Zone: "I think the majority will vote yes."
In a second national vote since Saddam was toppled in April 2003, Iraqis were asked one question: "Do You Approve the Draft Constitution of Iraq?"
However, under a deal reached Wednesday to try to bring disaffected Sunni Arabs on board, voters decided on what is effectively a partial constitution since politicians agreed that amendments could be considered after new elections in December.
Many Sunnis, who make up about 20 percent of Iraq's 26 million population, fear federal provisions in the charter could lead to the break-up of Iraq and leave control of its vast oil wealth in the hands of the majority Shias and the Kurds.
Saleh al-Motlaq, a Sunni spokesman for the National Council for Dialogue who had helped draft the charter, said he himself had voted 'no' because he was not satisfied with the result.
"I took part in the consultation and I voted 'no' to the constitution," he told AFP.