Election officials counted millions of paper ballots across Iraq (search) on Sunday to determine whether a surprisingly large turnout by Sunni (search) Arabs in the country's constitutional referendum had produced enough "no" votes to defeat the historic document.

Indications are that the constitution will pass, an elections commission official told The Associated Press (search), speaking on condition of anonymity because the counting was still going on.

But Abdul-Hussein al-Hendawi (search), a top official in the commission, stressed there were no results yet from Saturday's vote. "We cannot make any prediction, but we hope by tonight we will have an idea about the result of the vote," he said.

Initial estimates of overall turnout were 61 percent, election officials said. But competition appeared to have been more intense in the three most crucial Sunni-dominated provinces -- Diyala, Ninevah (search), Salahuddin, where more than 66 percent of voters were estimated to have turned out.

The constitution is a crucial step in Iraq's transition to democracy after two decades of rule by Saddam Hussein's dictatorship. Washington is hoping it passes so that Iraqis can form a legitimate, representative government, tame the insurgency and enable the 150,000 U.S. troops to begin to withdraw.

To defeat the constitution, Sunnis have to muster a two-thirds "no" vote in any three of Iraq's 18 provinces. They were likely to reach that threshold in the vast Sunni heartland of Anbar province in the west. Salahuddin (search) also looked possible. But getting the required votes in either Ninevah or Diyala (search) could be more difficult.

On Sunday morning, two mortar rounds hit Baghdad's Green Zone (search), the heavily fortified district where U.S. and Iraqi government offices are located, including the main center where all the votes from across the country are being counted. It was not clear if the mortars struck anywhere near the counting center. The blasts raised plumes of smoke from the zone but caused no injuries of significant damage, the U.S. Embassy said.

The attack came shortly after authorities lifted a driving ban imposed to try to prevent suicide car bombs during voting. The ban was part of a nationwide security clampdown on Saturday, which turned out to be one of Iraq's most peaceful days in months.

Iraq's Shiite Muslim (search) majority and significant Kurdish minority -- who control the National Assembly and government -- favor the constitution.

But many in the Sunni Arab minority, who controlled the country under Saddam Hussein, were pushing hard to defeat it. They fear the charter will break the country into three sections: powerful Kurdish and Shiite mini-states in the oil-rich north and south, and a weak and impoverished Sunni zone in central and western Iraq.

A nationwide simple majority in favor of the draft is assured. The nine provinces of the south, the heartland of the Shiites, and the three provinces of the Kurdish autonomous zone in the north were expected to roll in big "yes" numbers.

If the constitution fails, a new constitution must be drafted by a new parliament, to be elected in December. If it passes, a new parliament will also be elected and a new government selected -- the first permanent, fully constitutional government in Iraq since collapse of Saddam Hussein's (search) rule in 2003.

In Baghdad, Adel al-Lami (search), the elections commission head, said that as counters in the Green Zone were working through results from areas closer to Baghdad but still waiting for results and ballot boxes to arrive from provinces farther out.

Each province counts its own votes, then sends a report of the results to Baghdad, along with the ballot boxes. In Baghdad, the count is checked, then compiled.

In Karbala (search), a Shiite province just south of Baghdad, some 440,000 people voted -- a 60 percent turnout -- and 95 percent of them cast "yes," ballots, according to the head of the election commission office in the province, Safaa al-Mousawi.

An official in the main Shiite political party in the ruling coalition, the Supreme Council for the Islamic Revolution (search) in Iraq, said that the southern Shiite provinces of Najaf and Basra and Baghdad, which has a mixed population, together voted 90 percent "yes." But the official, Haitham al-Husseini (search) did not break down the result in each province.

Still, no matter what the nationwide turnout, the constitution will fall if Sunni Arabs achieve the two-thirds "no" vote in three provinces. They have a chance of getting it in Salahuddin, Ninevah and Diyala because they have a Sunni Arab majority population. But they also have significant Shiite or Kurdish communities, making it difficult to reach the two-thirds.

Western Anbar provinces has almost no Shiites or Kurds, so it is likely to easily reach the threshold.

There were suggestions Salahuddin could also reject the constitution after a strong turnout by Sunni Arabs, particularly in the town of Tikrit (search), Saddam's birthplace. Initial election commission figures said around 78 percent of the Salahuddin's votes came from Sunni Arab towns, almost all of which are likely to be "no."

Diyala and Ninevah may be harder to nail down for the Sunni Arab opponents of the constitution. Ninevah -- with its capital Mosul (search), Iraq's third biggest city -- has an extremely mixed population of Shiites, Kurds, Christians, Turkomen and others along side a Sunni Arab majority. In Diyala, the Shiite and Sunni populations are more intermingled than in other regions.

Whether the charter passes or fails, Sunnis appeared to throw themselves wholeheartedly into a political process that until now they have been deeply suspicious of.

That could indicate they will turn away from support of the insurgency and try in the future to work within a system U.S. and Iraqi leaders hope can moderate the country's vicious sectarian divisions.

But if the constitution passes despite a significant Sunni "no" vote, hard-liners in the community could decide the insurgency is their only hope of retaining influence in the country.

It had been feared that insurgents would launch a wave of attacks during the referendum, but, with the help of extraordinary security measures, it was relatively peaceful. Several shooting or bomb attacks on polling stations wounded seven voters. Four Iraqi soldiers were killed by bomb blasts for from polling sites.

Armed insurgents burst into two polling stations -- one on the outskirts of Baghdad, the other in the western town of Khalidiyah (search) -- after voting ended, stealing filled ballot boxes. They also kidnapped 10 election workers from the Khalidiyah station, and tribal leaders were trying to negotiate their return.