The main Arab Sunni alliance that contested Iraq's election said on Saturday it had been a success, fuelling US hopes peaceful politics will help pave the way for a troop withdrawal.
Washington and its allies in the Shi'ite and Kurdish-led government have been trying to lure Sunnis into the political process, hoping to undercut support for the Sunni insurgency.
"The election process succeeded ... Thank God there were only a few cases in a huge country where there is death and violence," Adnan al-Dulaimi, leader of one of the parties in the Iraqi Accordance Front, told a news conference.
The US military and rebels have warned that a truce during Thursday's election that allowed Sunnis to vote did not mean attacks aimed at removing US troops would end.
But US President George W. Bush was buoyed by the millions who turned out to vote and he praised them for "defying the terrorists and refusing to be cowed into not voting".
In stark contrast to bloody polls in January, the election was largely peaceful, with turnout swelled by the participation of Sunnis sidelined by a previous boycott.
Iraqi electoral officials do not expect final poll results for at least two weeks. The ruling Shia bloc is expected to face fierce competition from US-backed secular politician Iyad Allawi.
Members of Allawi's Iraqi National List told a news conference there were violations at several polling stations, including Iraqis voting under the names of dead people.
Independent Electoral Commission chief Hussein Hendawi told a news conference that there would be no need for recounting of votes in any polling station after he was asked about complaints of violations in the former rebel stronghold of Falluja.
In the wake of the election, US forces in Iraq are likely to shrink from a current 155,000 to their pre-election total of 138,000 by early February. But other reductions are contingent on US commanders deciding that Iraqi forces are trained sufficiently to fight the insurgency on their own.
Bush will tell Americans in an Oval Office address on Sunday that the US mission in Iraq has entered a critical period in the aftermath of the election, the White House said on Friday.