"The terrorists now know that they cannot win," Ayad Allawi said Monday in his first press conference since Sunday's vote.
"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 promised to work to ensure that "the voice of all Iraqis is present in the coming government."
Individual polling stations completed a first-phase count of ballots Monday. Local centers will then prepare tally sheets and send them to Baghdad, where vote totals will be compiled, election Commission official Adel al-Lami said. Final results could take up to 10 days.
By the time the polls closed Sunday night much of Iraq had become a huge street party, reports CBS News Anchor Dan Rather from Baghdad. Turnout was the key; officials estimate about 60 percent of the 14 million eligible voters cast ballots.
While they didn't provide any numbers, election officials said turnout in hard-line Sunni areas was better than some had expected. However, a U.S. diplomat said participation by Sunni Arab voters was low – raising fears that the group that drives the insurgency could grow ever more alienated.
In other developments:
Although turnout figures were unavailable, a U.S. diplomat briefing reporters on condition of anonymity said "good anecdotal information" indicated that "Sunni participation was considerably lower than participation by the other groups, especially in areas which have seen a great deal of violence."
In the heavily Sunni town of Tikrit, Saddam Hussein's hometown, 48-year-old history teacher Qais Youssif said no member of his family had voted.
"The so-called elections were held in the way that America and the occupation forces wanted," Youssif said. "They want to marginalize the role of the Sunnis. They and the media talk about the Sunnis as a minority. I do not think they are a minority."
The electoral commission said Sunday it believed overall turnout 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. However, the commission backtracked later on turnout estimates and said none would be available until the count was complete.
While there was considerable violence, the absence of any catastrophic single attack Sunday seemed at least partly a result of the heavy security measures, including a ban on most private cars. At least 44 people were killed in election day attacks, eight of them suicide bombers who moved on foot, blowing up near polling sites in Baghdad.
Two U.S. service members also died in fighting in the Sunni stronghold of Anbar province west of Baghdad Sunday.
It was still unclear if the successful vote would deal a significant blow to the insurgents or 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.
But one of the many Marines involved in providing security for the election says the high turnout contained a message for Iraqi insurgents.
"They think they have the support of the people," said Lt. Col. Bob Durkin, of the 1st Battalion, 2nd Marines, 24th Expeditionary Unit, in a CBS News interview. "They [the insurgents] have to see that they don't."
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."
The top opponents to the U.S.-led invasion of Iraq had praise for the vote, though with reservation. French President Jacques Chirac phoned Mr. Bush and said he was satisfied by Iraqi participation in the vote. "These elections mark an important step in the political reconstruction of Iraq. The strategy of terrorist groups has partly failed," Chirac said, according to a spokesman.
Russian President Vladimir Putin called the election an "historic event for the Iraqi people because it is undoubtedly a step toward democratization of the country."
But his Foreign Ministry expressed regret over the low Sunni turnout, echoing worries expressed by several world leaders. It warned of difficulties "if other political forces feel removed from state affairs."
Sunday's historic election came 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.
The ticket endorsed by the Shiite Grand Ayatollah Ali 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.
In comments to CBS News' Face The Nation, Secretary of State Condoleezza Rice would not say whether U.S. forces would leave the country in great numbers now that the vote is complete. President Bush also did not mention any U.S. military withdrawals in his statement.