International observers have praised the organisers of Iraq's parliamentary election, which they said generally met international standards.
The results of the poll could take up to two weeks to be confirmed
A spokesman for the International Mission for Iraqi Elections conceded that there had been minor problems, but said the vote had generally gone well.
About 11m Iraqis were estimated to have voted, a turnout of about 70%, with results due in two weeks or more.
President Bush is to make an address on the situation in Iraq on Sunday night.
"We are now entering a critical period for our mission in
Iraq, the president will talk about what we have accomplished
and where we're headed," said his spokesman, annoucing the rare address from the Oval Office, to be made at 2100 on Sunday (0200GMT Monday).
"The Independent Electoral Commission of Iraq is to be commended on the way it has performed its role under the difficult circumstances prevailing in Iraq," said Paul Dacey, spokesman for the international observers.
Iraq's staging of major elections in January, October and December would have been a major challenge even for well-established democracies, Mr Dacey said.
IRAQ ELECTION FACTS
275-seat National Assembly will have four-year term
18 provinces are taken as separate constituencies
230 seats allocated according to size of population
45 seats distributed to parties whose ethnic, religious or political support is spread over more than one province
Some 15 million eligible to vote
One third of candidates in each party must be women
The country's electoral commission announced on Friday that 320,000 Iraqis living abroad voted in the election.
Around 15 million Iraqis were eligible to vote for the country's first full-term government since Saddam Hussein was ousted in 2003.
The vote will elect 275 members of a national parliament, who will in turn appoint a president.
Voting was extended in many parts as Sunni Arabs took part after boycotting previous elections.
Election officials reported high turnouts even in Sunni insurgent strongholds such as Falluja and Ramadi.
The voting took place amid a massive security operation, with 150,000 Iraqi troops and police deployed and borders and airports closed.
US President George W Bush described the vote as "historic", and appeared delighted with the high turn out.
Sunni nationalist insurgent groups had urged people to vote to prevent the election of a government dominated by Shias and Kurds.
However, the al-Qaeda in Iraq group denounced the election and threatened attacks. Two civilians and a US marine were slightly injured in morning attacks.
The new national assembly will replace the transitional government elected in January. Some 6,655 candidates, 307 parties and 19 coalitions registered for the ballot.