Iraq's interim Prime Minister Iyad Allawi has hailed Sunday's election as a "victory over terrorism".
Iraqis queued to vote in the former rebel stronghold of Falluja
He spoke as the UN's senior election official said turnout in Sunni areas - where the insurgency has been strongest - was higher than expected.
However he stressed that voting among Sunnis, whose participation in the poll is seen as key to the success of the new government, was nonetheless low.
But regardless of whether they voted, Mr Allawi said, Iraqis must now unite.
"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 in his first remarks since Sunday's elections for a transitional national assembly.
The overall election turnout has been estimated at about 60%, with some eight million Iraqis voting. It remains unclear how many Iraqis were registered to vote.
Almost 94% of more than a million Iraqis living abroad who were registered to vote cast their ballot, the International Organisation for Migration (IOM), which was appointed by Iraq's electoral commission, said.
The UN's senior election official in Iraq, Carlos Valenzuela, told BBC News he was pleased that more people than expected "defied the threat of violence to go and vote".
He said a precise turnout figure would not be known for several weeks, but it appeared higher numbers of Sunnis than expected turned out to vote.
He said some areas reported a better turnout than others.
Queues, for example, were seen forming outside polling stations in the former rebel stronghold of Falluja.
But voting figures were thought to be very low in Ramadi and Samarra. Four polling booths in the Sunni Azamiyah district of Baghdad never even opened, according to reports.
Long count ahead
Leading Sunni politician Adnan Pachachi, who had called for the elections to be postponed, said he was glad his expectations about low turnout were not borne out.
He said he wanted Sunni parties that had not taken part in the elections to be involved in the writing of the Iraqi constitution.
Results due in around 10 days
Early March: PM appointed
Late March: Government formed
15 August: Draft constitution (six month extension possible)
15 October: Possible referendum on constitution
By 15 December: Elections for government
"This is the most important task before the national assembly," said the former Iraqi foreign minister. "If that can be done I think we would have paved the way for a much more inclusive election before the end of the year."
The BBC's Paul Wood, in Baghdad, says defeating the insurgency may depend on being able to form a broad-based government which Sunnis feel represents their interests, as well as the Shias who voted in such large numbers.
He says votes were counted through the night, sometimes by candlelight because of electricity cuts.
It may be 10 days yet before the final tally is ready, he adds.
Mr Allawi said that once the results are known, the new 275-member National Assembly will work to name a prime minister and new government.