No firm official figures were available, but Iraqi election authorities said preliminary estimations were that about 8 million people, or roughly 60 percent of registered voters, may have taken part in the voting yesterday.
No figures on turnout among Iraq's Shi'ite Muslim, Sunni Muslim, and Kurdish communities were immediately available.
Outside Iraq, officials said some 250,000 expatriate Iraqis had cast votes in 14 countries.
Iraqi government officials and U.S. leaders praised Iraqis for casting ballots despite a series of insurgent suicide bombings and other attacks, mainly in Baghdad, that killed more than 40 people, including nine attackers.
U.S. President George W. Bush called the vote a "resounding success" and said Iraqis, by participating in free elections, had rejected the antidemocratic ideology of terrorists.
"By participating in free elections, the Iraqi people have firmly rejected the antidemocratic ideology of the terrorists. They have refused to be intimidated by thugs and assassins. And they have demonstrated the kind of courage that is always the foundation of self-government," Bush said.
UN Secretary-General Kofi Annan said Iraqis had shown courage in effectively organizing and carrying out the elections within a limited timeframe and under difficult circumstances.
In a written statement, Annan called for reconciliation among all Iraqis and urged that those who were unable or unwilling to take part in the elections now be brought into the constitution-making process.
(Reuters/AP/AFP)For news, background, and analysis on Iraq's historic 30 January elections, see RFE/RL's webpage "Iraq Votes 2005."