Officials in Iraq say there is a possibility that partial results could be released on Sunday, but complete ballot counting in Saturday's constitutional referendum is expected to take up to five days.
Election officials said turnout was heavy in at least eight of Iraq's 18 provinces, while another seven provinces reported moderate turnout. Preliminary estimates indicate more than 60 percent of eligible voters cast their ballots.
They were able to cast a yes or no vote on whether to approve the draft constitution.
A simple majority will pass the constitution, but it could fail if two-thirds of voters in at least three provinces reject it.
While some sporadic violence marred the day, Saturday was one of the most peaceful days in Iraq in months. In the day's most serious incident, a roadside bomb killed three Iraqi soldiers.
Thousands of Iraqi security forces and police, as well as U.S.-led coalition troops, will continue to enforce strict security measures through Sunday.