Iraqi officials say there could be some preliminary results available in a day or two. But a complete official count is expected to take longer.
Estimates put the turnout for the referendum at about 10 million voters, or more than 60 percent of the electorate -- a turnout that world leaders praised as courageous in view of the ongoing insurgency.
Iraqis this morning also were reflecting on the way the referendum was conducted. One Baghad police officer said he is satisfied with a massive security clampdown by U.S. and Iraqi forces that prevented major attacks during the vote after months of militant bloodshed.
"The referendum process yesterday took place in a calm atmosphere and security clampdowns prevented explosions and chaos. Iraqis turned out to vote in a referendum that was free and democratic," he said.
A Baghdad resident said he was satisfied with the way the referendum was conducted. He also said he thinks Iraqis understood the significance of the vote. "When I went to the polling center, I found that everything was organized," he said. "No one forced us to write 'yes' or 'no.' We chose. So I do not think that any Iraqi would write 'yes' or 'no' without having any idea about the constitution."
Another Baghdad resident said today that he also is satisfied with the organization of the vote. "Members of the election commission facilitated everything to the citizen and explained to us some points and paragraphs in the constitution."
Iraqi Foreign Minister Hoshyar al-Zebari told RFE/RL he thinks a last-minute agreement reached with some Sunni Arab leaders helped improve the turn out significantly in the face of a boycott called by other Sunni leaders.
That last-minute deal will allow a parliament due to be elected in December to make further amendments to the draft constitution.
"Irrespective of the outcome it is my belief that this is the first time we have been allowed to decide our own constitution and future by ourselves without pressures or coercion but in complete freedom. This draft is not the end of the road. There will certainly be amendments but the basic principles in terms of freedoms and rights, will remain," al-Zebari told Radio Free Iraq.
Correspondents in Sunni-dominated towns like Al-Fallujah, Mosul, and Tikrit say Sunni voters appeared to have turned out in force to cast ballots. The charter requires a simple majority for approval but would be rejected if a two-thirds majority in at least three of the country's 18 provinces vote "no."
U.S. President George W. Bush said in his weekly radio speech yesterday that by casting their ballots, Iraqi voters dealt a severe blow against the Iraqi insurgency and terrorism.
"This weekend's election is a critical step forward in Iraq's march toward democracy. And with each step the Iraqi people take, Al-Qaeda's vision for the region becomes more remote," Bush said.
Members of Iraq's majority Shi'ite community danced in the streets after voting ended last night.
Meanwhile, several mortar rounds today landed in the high-security area of Baghdad known as the Green Zone, which contains diplomatic and military installations. There was no immediate word on any casualties.For RFE/RL's full coverage of Iraq's constitutional referendum, see "Iraq Votes 2005"