An initial result forecast might be available within two days, with an unofficial tally on Thursday and a final announcement on 24 October, although that timeframe could change, senior electoral official Farid Ayyar said on Sunday.
During Saturday's referendum, five US Army soldiers were killed by a roadside bomb, the military said Sunday.
The vehicle the five soldiers were riding in was hit by a roadside bomb in the mostly Sunni Arab city of Ramadi, 115km (70 miles) west of Baghdad.
The five soldiers, assigned to the 2nd Brigade Combat Team, 2nd Marine Division, II Marine Expeditionary Force (Forward), were not identified pending notification of their relatives.
The vote of the Iraqis on the future of their country, and indirectly on how long US-led troops would remain in Iraq, came off without the widespread violence that marred general elections in January.
Iraqis let off celebratory gunfire and Shia danced in the streets of Baghdad after the polls closed, anticipating what they believed was certain approval of the country's first constitution since the fall of Saddam Hussein's government.
"Our constitution has been approved, down with the Baathists!" chanted a joyful crowd, referring to members of Saddam's disbanded political party.
Jalal Talabani was optimistic
most Iraqis would vote yes
Shia and Kurds, who were oppressed during Saddam's leadership, were expected to have massively approved the draft document.
But attention focused on Sunni Arabs, many of whom fear domination by a Shia-Kurd alliance and loss of crucial oil revenues.
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.
According to a preliminary estimate, more than 61% of registered voters cast ballots amid tight security.
The vote was hailed by leaders worldwide, with US President George Bush saying: "By casting their ballots, the Iraqi people deal a severe blow to the terrorists and send a clear message to the world: Iraqis will decide the future of their country through peaceful elections, not violent insurgency."
Sunni Salih al-Mutlaq helped draft
the charter but voted against it
Secretary of State Condoleezza Rice said on Sunday that Iraqis had probably approved the draft charter.
"Most people assume on the ground that it probably has passed," Rice told reporters during a visit to London.
Basing her figures on reports from officials in Iraq, she said the overall turnout was about 63%-64%.
In Japan, a Foreign Ministry statement said: "We pay tribute to the interim government and people of Iraq who participated in the national referendum despite security issues and other difficult conditions."
Australian Foreign Minister Alexander Downer added: "It's a triumph for ordinary people over militants."
Iraqi President Jalal Talabani, a Kurd, had forecast victory as he cast his vote on Saturday inside the Green Zone, saying: "I think the majority will vote yes."
But Salih al-Mutlaq, a Sunni spokesman for the National Council for Dialogue who had helped draft the charter, said he himself had voted no because he was not satisfied with the document.
"I took part in the consultation and I voted no to the constitution," he said.
In the second national vote since Saddam was toppled in April 2003, Iraqis were asked one question: "Do you approve the draft constitution of Iraq?"
Despite tight security during
voting, attacks killed six people
The draft is likely to be quickly amended once a new round of general elections are held, and US Middle East expert Juan Cole from the University of Michigan called the document "fluid and changing".
"It is not even necessarily parliament that changes it... It is the clan and community leaders," he noted, since a last minute deal on the document had been spearheaded by Kurdish leader Massoud Barzani and approved by leaders of other Iraqi groups before it was approved by parliament.
"This vote is sort of a national vote of confidence for that leadership," Cole said.
To reach polling stations, voters passed through three rings of security, including concrete road barriers, rolls of razor wire and searches by squads of police.
A ban on any civilian vehicles circulating on voting day was part of elaborate security measures taken to prevent attacks by fighters, and Baghdad resembled a baking, dusty ghost town throughout the day.
Despite the precautions, including the closure of international borders, six people died in various attacks, including three Iraqi soldiers who were killed in a bomb blast as they inspected a polling station northeast of the capital.
For the most part, however, voting was peaceful and the casualty toll was far less than the 36 deaths when Iraqis elected a national parliament on 30 January.
In al-Anbar province, 10 workers for the Iraqi Independent Electoral Commission were abducted while heading to work at the polls, and sabotage on power lines cut electricity to Baghdad and the southern city of Basra.
Approval of the draft constitution would pave the way for parliamentary elections in December, which the Bush administration hopes will help weaken fighters and allow a gradual pullout of the 140,000 US soldiers deployed in Iraq.
Nearly 2000 US soldiers have died in Iraq since the war was launched and the war has become increasingly unpopular in the US.