Polling stations in Iraq finished Monday the first-phase count of millions of ballots cast Sunday in historic elections to determine how a post-Saddam Hussein Iraq will look.

The counting took place as interim Prime Minister Iyad Allawi (search) called on his fellow Iraqis to set aside their differences and come together. Allawi also told reporters in a news conference that the election should send a signal to the insurgents.

"The terrorists now know they cannot win," he said.

From the counts by individual stations, local centers will prepare tally sheets and send them to Baghdad, where vote totals will be compiled, Electoral Commission official Adel al-Lami said. Final results could take up to 10 days.

With turnout in the vote still unknown, concern was focused on participation by Iraq's Sunni Arab minority, amid fears that the group that drives the insurgency could grow ever more alienated. Electoral Commission officials said turnout in hardline Sunni areas was better than some expected, thought they cited no numbers. A U.S. diplomat warned that Sunni participation appeared "considerably lower" than that of other groups.

Meanwhile, Arab TV channel Al-Jazeera aired a video on Monday that showed insurgents walking amid the wreckage of an airplane that was said to be that of a British C-130 that crashed in Iraq Sunday. All 10 military personnel on board the transport plane were missing and presumed dead, making it Britain's single largest loss of life since the war began.

On Sunday, Ansar al-Islam (search) claimed on an Islamic Web site that its fighters tracked the aircraft, "which was flying at a low altitude, and fired an anti-tank missile at it."

Despite fears of growing violence, the nation was calm Monday as vehicles again wove their way down Baghdad's streets after an election-day ban on most traffic.

Security throughout the country was still tight on Monday. The city's main bridges were blocked, indicating some security was still in place. A string of insurgent attacks and eight homicide bombings killed 44 people on Sunday.

Final results of the election weren't expected for days, but the country was already focusing on goals almost as challenging as the election itself: forming a new governing coalition, writing a constitution and winning popular trust.

The electoral commission said it believed, based on anecdotal information, that turnout overall among the estimated 14 million eligible Iraqi voters appeared higher than the 57 percent, or roughly 8 million, that had been predicted before the vote. But it would be some time before any precise turnout figure was confirmed, they said.

Allawi urged factions within Iraq to come together, aiming his comments at Iraq's Sunni minority, a large percentage of whom avoided the polls Sunday.

"We are entering a new era of our history and all Iraqis — whether they voted or not — should stand side by side to build their future," he said. "Now is a suitable time for us to work together so that the whole world can watch the capabilities of this great country."

The election will almost certainly bring to power the country's long-suppressed Shiite Muslims (search), who make up 60 percent of Iraq's population, boosting the sect's influence and worrying neighboring countries with Sunni majorities.

The main Shiite clerical-backed faction in the race was already claiming a strong showing in the election. Officials of the United Iraqi Alliance (search) said they expected to win at least 45 percent — and maybe even a slim outright majority — of seats in the 275-member National Assembly. Local officials of the parties within the alliance said the list swept some southern cities, winning 90 percent of the votes in Najaf and 80 percent in Basra.

The claims could not be confirmed, and the Alliance had been expected to run strong in the Shiite heartland. Going into the vote, the list headed by Allawi was also considered a main contender.

A powerful showing for the Alliance, which was endorsed by the Shiite Grand Ayatollah Ali al-Sistani (search), could make Sunnis even more reluctant to accept the results of the election — particularly if Sunni participation turns out to have been low.

Security just after the ballots are counted will be crucial, because once the winners are announced, they will likely become terrorist targets.

Not even the country's frequent power outages could stop the electoral process, the first free vote in a half-century. In the Shiite holy city of Najaf (search), election workers began their task crouched on the ground, counting ballots by the glow of an oil lamp.

"Now I feel that Saddam is really gone," said Fatima Ibrahim, smiling as she headed home after voting in Irbil (search), in the Kurdish northern region. She was 14 and a bride of just three months when her husband, father and brother were rounded up in a campaign of ethnic cleansing under Saddam. None have ever been found.

It was still unclear if the successful vote would deal a significant blow to the insurgents, or rather lead to a short-term rise in violence. The militants might need time to regroup after the spate of attacks they launched in the weeks before the vote.

The election was hailed as a success around the globe, with President Bush declaring: "The world is hearing the voice of freedom from the center of the Middle East." Australian Foreign Minister Alexander Downer said Iraqis showed "the courage to stand up to [violence] and we should support them."

In Europe, both opponents and supporters of the Iraq war came together to praise the election, and the European Union's foreign policy chief said the milestone would pay off with more aid.

"They are going to find the support of the European Union, no doubt about that, in order to see this process move on in the right direction," Javier Solana (search), the EU's foreign and security representative, told The Associated Press.

France and Germany, two of the strongest critics of the U.S.-led mission in Iraq, also welcomed the seemingly strong election turnout. A statement sent out by the German government described it as a sign of "the firm determination of the majority of Iraqis" to take charge of their nation's future.

But some cautioned that it was too early to declare the election a total success. New Zealand Foreign Minister Phil Goff said a low Sunni turnout could still impact the new government's ability to bring the frail nation under its control.

"Ways must be found to involve Sunnis in the drafting of the constitution, which will define power among Iraq's disparate groups, and to give them a stake in the new government," he said.

Sunday's historic election came only seven months after Iraq's interim government took over from a U.S.-led coalition, and less than two years after Saddam's ouster.

The 275-member National Assembly, elected for an 11-month term, will draft a permanent constitution, and if the document is approved, Iraqis will vote for a permanent government in December. If the document is rejected, Iraqis will repeat the whole process again.

Uncertain Sunni turnout, a string of insurgent attacks and eight suicide bombings that killed 44 people, and the crash of the British military plane drove home that chaos in Iraq isn't over yet.

Iraq's interior minister, Falah al-Naqib, said Monday that insurgents used a handicapped child as one of the suicide bombers. He added that a total of 38 attacks were carried out against polling stations across the country.

The ticket endorsed by al-Sistani was the pre-voting favorite, while Allawi's slate was also considered strong. Once results are in, it could take weeks of backroom deals before a prime minister and government are picked by the new assembly.

If that government can draw in the minority Sunni Arabs who partly shunned the election, the country could stabilize, hastening the day when 150,000 U.S. troops can go home.

With the polls barely closed, international debate immediately turned to just that issue. On Monday, Senate Democratic Leader Harry Reid plans to call on Bush to outline an exit strategy for Iraq. And Downer said his country will keep troops only if the country's newly elected government wants them.

Iraq's interior minister, Falah al-Naqib, told Britain's Channel 4 News he expected there would be no need for U.S. troops any longer than 18 months because that's when he anticipates Iraq's security forces will be trained well enough to handle the job themselves.

But Allawi said recently that it was premature to know when Iraqi troops would be ready.

Across the largely authoritarian-ruled Arab world, where dislike and distrust of U.S. power and American intentions dominates the public debate, some dismissed the poll as a U.S.-orchestrated sham. Others hoped it might prove a catalyst for a region-wide democratic push.

Egyptian President Hosni Mubarak — sure to win his own country's much-less-democratic vote later this year — telephoned Allawi to congratulate him on the smooth election, saying he hoped it would "open the way for the restoration of calm and stability" in Iraq.

FOX News' Andrew Stack and The Associated Press contributed to this report.