Sunni Arab, Shiite and Kurdish concerns were reflected among many of the Iraqis living in neighboring countries, Europe and the United States. Voters came from all stages of their country's stormy past: those who fled Saddam Hussein's regime, others who left amid the 2003 U.S.-led invasion or took refuge abroad from the relentless bloodshed that followed.
An estimated 240,000 Iraqi-Americans are believed eligible to cast their votes. Sandra McNeill of CBS radio station WWJ-AM reports there are two election sites in Detroit, and an organizer expects at least twice as many voters as last year, when bad weather and poor choice of sites kept many voters away.
Iyad al-Iraqi, 22, a Sunni Arab voting in the Jordanian capital, Amman, said he hoped the elections would bring more "Muslim Arabs" to power.
"We hated living under Saddam, but at least it was safer then. Give us a thousand like Saddam, but not a single American to rule us," he said.
In other developments:
Sunnis at home and abroad largely shunned Jan. 30 elections for an interim parliament that wrote the nation's constitution, Iraq's first free vote in decades. The result was a legislature dominated by members of the Shiite Muslim majority and the strong Kurdish minority.
This time Sunnis in Iraq were pressing for a strong turnout to build their numbers in the 275-member legislature, and the response in predominantly Sunni Jordan and Syria suggested the communities there were answering the call.
Voting also appeared heavy among Iraqis in mainly Shiite Iran, a close ally of the Shiite parties that control the current government in Baghdad. Hundreds lined up at a polling station in southern Tehran to cast ballots.
In Qom, a center of Shiite religious studies, Iraqis, most of them clerics studying at seminaries, also converged at polling stations, the official Islamic Republic News Agency said.
A group of 50 Kurdish men traveled by bus from the English town of Ipswich to London, waving Kurdish flags and singing nationalist songs at a polling center. "We want to see Kurdistan become independent," said 28-year-old factory worker Dilzar Muhamad. "We don't worry about what will happen to the Arabic people in the rest of Iraq, or about Turkey or Iran for that matter."
Some 1.5 million Iraqis living abroad are eligible to vote at polling centers in 15 countries, including the United States and Canada. Tuesday was the first of three days of expatriate voting, while Iraqis at home will go to the polls on Thursday.
In Syria, home to 400,000 Iraqis, thousands flocked to 11 polling stations across the country. Hayel Youhana, the supervisor of one polling center in Damascus, declined to give figures but said the turnout "surpassed our expectations."
Talal Shawkat, 55, a Baghdad native who has lived in Damascus for the past 18 months, said: "I want to vote because I see the process as free and honest."
In Zarqa, Jordan, the hometown of Iraq's most feared terror leader Abu Musab al-Zarqawi, Iraqis turned up at polling stations despite a statement issued hours earlier on the Internet by al-Zarqawi's al Qaeda in Iraq and four other militant groups branding the polls a "satanic project" that violated God's law.
"What they say is bogus," Hamed Al-Nasseri, 56, shouted outside a polling station in Zarqa, an industrial city 20 miles northeast of Amman. "I'm voting to challenge these militants, to have a strong parliament and government that would restrain these outlaws."
Baha'a Eldin, 53, an Iraqi social worker whose son was kidnapped briefly by criminals after the U.S.-led invasion, said in Amman that he hoped the polls will put an end to "sectarianism and tribalism" and allow for safer conditions "so we can return to our country and live in peace."
Haidar Al Latif drove 10 hours in a rented car from South Dakota to a polling place in suburban Chicago.
"This is the first time I had the opportunity to vote," said Al Latif, 34, who works as a mason in Sioux Falls. He said a snowstorm prevented him from making the trip in January.
Campaign posters also dotted polling stations across Europe.
In Denmark, Soran Abul-Aziz spent the night outside a polling station in a sleeping bag. He said he wanted to be the first one to cast his ballot.
"I am very happy. I hope Iraq soon will become a democratic country like Denmark," he said, sporting a red Santa hat.
The countries hosting the vote were chosen because they had the largest concentrations of Iraqis: Australia, the United States, Britain, Canada, Denmark, France, Germany, Austria, Iran, Jordan, the Netherlands, Sweden, Syria, Turkey and United Arab Emirates.