BAGHDAD, Iraq (CNN) -- As election workers in Iraq counted millions of paper ballots cast in the constitutional referendum, U.S. Secretary of State Condoleezza Rice said Sunday the measure "had probably passed" but cautioned she didn't know the final outcome.Rice told reporters traveling with her in London that she had spoken Sunday with U.S. Ambassador to Iraq Zalmay Khalilzad and her comments were based on "the assessment of people on the ground." "There is a belief that it has probably passed," Rice said. But minutes after Rice made the comments, a State Department spokesman said Rice also wanted to emphasize that "we don't know" how the referendum will turn out.Spokesman Sean McCormack said Rice had talked to Khalilzad after the press briefing, and her later clarification that the final outcome was unknown was not backtracking from her earlier assessment.Khalilzad told CNN's "Late Edition" Sunday that it was too early to predict the outcome."We'll find out tomorrow," he said from Baghdad.Meanwhile, the U.S. military reported that a roadside bomb Saturday killed five U.S. soldiers near Ramadi, west of Baghdad in Anbar province.The soldiers were assigned to the 2nd Brigade Combat Team, 2nd Marine Division, II Marine Expeditionary Force (Forward).In another incident, a homemade bomb killed a U.S. Marine on Saturday in Saqlawiya, northwest of Falluja, the U.S. military said. The U.S. death toll in the Iraq war now stands at 1,980.The body of a British officer was found Saturday where he had been based in Basra, a Ministry of Defense statement said. Capt. Ken Masters was commanding officer of the special investigation branch of the Royal Military Police responsible for investigating serious war-zone incidents. No cause of death was cited.Count to take daysThe vote-tallying, which involved more than 5,800 polling stations, is expected to take days and results aren't expected until next week.(See the view from the day after the vote)The referendum was being hailed as a success, because turnout appeared to be high enough to legitimize the outcome and there was little violence. (Watch how people voted -- 2:33)"The draft constitution was voted yesterday by the overall majority of the Iraqi people," Iraqi Foreign Minister Hoshyar Zebari told CNN. "And all the indications we are getting, even from those provinces where the vote may swing, are encouraging and positive -- as for a 'yes' vote for this constitution." About 15.5 million of Iraq's 26 million people were registered to vote. (A look at what's at stake -- 3:08)Although she said several times that the referendum had "probably passed, Rice also said Sunday that it would not be a crisis if the constitution failed. "It's not a setback for the Iraqis if they exercise that right one way or another," she said. "It is a process that is alive and well." Sunnis came outA spokesman for the Iraqi electoral commission said Saturday initial figures showed more than two-thirds of eligible voters cast ballots in Baghdad and seven other provinces and in eight others turnout ranged between 33 percent and 66 percent.Election officials had no information about Anbar province in western Iraq, which has been a hotbed of insurgent violence. Turnout in the southern province of Qadisiya was projected to be less than 33 percent, said Fareed Ayar, a spokesman for Iraq's Independent Electoral Commission. In January, when Iraqis elected an 275-member interim National Assembly, about 60 percent of the registered voters turned out nationwide. Sunni Arab leaders actively boycotted that vote and found themselves with little voice in government. By contrast, strong participation was reported Saturday in some of the Sunni Arab areas where voters were scarce in January."It's very important to focus now on the success that was achieved yesterday, with the participation of the Sunnis," Khalilzad said. "Now, it is clear that the Sunnis have confidence in the process -- and that's demonstrated by their participation." Bush reaction to the votePresident Bush hailed the Iraqi referendum vote, saying Sunday the apparently strong turnout and decrease in violence from the last election were signs of "progress toward peace.""This is a very positive day for the Iraqis and as well for world peace," he said. "Democracies are peaceful countries."Bush said the referendum "stands in stark contrast to the attitudes and philosophy and strategy of al Qaeda and its terrorist friends and killers."Election workers abductedIraqi soldiers and police had protected voting sites, while U.S. and coalition forces were on standby. Vehicles were barred from the streets, so voters walked to the polls. (Watch last-minute preparations -- 2:24)Despite the security, 10 election workers were kidnapped from two towns in Anbar province Saturday morning, an election official announced Sunday. Tribal leaders are mediating the negotiations for the workers, who were abducted in Khalidiya and Jazira, Ayar said.Iraqi police said a sniper killed a civilian at a western Baghdad polling station. The sniper, who may have been targeting police, escaped. A roadside bomb wounded two Iraqi police officers near a polling station in Baghdad shortly after voting started, a police official said. And 11 gunmen stole five ballot boxes from a Baghdad polling place a half hour after polls closed at 5 p.m. Police said it was unclear how many ballots were stolen.How the vote must goThe draft constitution -- hammered out after months of contentious, painstaking negotiations by the National Assembly -- must be approved by a majority of Iraq's voters.However, the constitution would fail if it is rejected by at least two-thirds of the voters in at least three of the country's 18 provinces. With many Sunni Arab groups opposing the document, rejection was considered possible in four provinces where Sunnis predominate. (Full story)If the constitution is approved, Iraqis would vote in December for a permanent government.If constitution is rejected the transitional assembly would be dissolved and the constitution process would begin anew after the December elections.CNN's Christiane Amanpour, Dana Bash, Arwa Damon, Kevin Flower, Andrea Koppel, Octavia Nasr, Aneesh Raman, Nic Robertson and Mohammed Tawfeeq contributed to this report.