WASHINGTON – Defying threats of suicide bombers and assassinations, millions of Iraqis went to the polls yesterday in the country’s first free and fair nationwide election since 1953.

Praising the commitment of Iraqis to reject the “anti-democratic ideology of the terrorists,” President Bush said in a statement from the White House that “The world is hearing the voice of freedom from the center of the Middle East.”

Wire reports from Baghdad said the streets were for the first time in months filled with children playing soccer in many parts of the besieged capital. Voters proudly displayed their fingers stained in blue ink to prove they had voted and prevent them from voting twice.

One report from Iraq said a 90-year-old woman was pushed to a Baghdad polling station on a wheelbarrow. Another said that women who had survived Saddam Hussein’s 1988 campaign against the Kurds were celebrating at polling places in northern Iraq. Mr. Bush quoted a dispatch about a man who had lost a leg in a terrorist attack last year. “I would have crawled here if I had to. I don’t want terrorists to kill other Iraqis like they tried to kill me. Today I am voting for peace,” Mr. Bush quoted him as saying.

The Associated Press quoted an Iraqi election official, Mijm Towirish, as saying his country had “broken a barrier of fear.” CNN quoted Iraq’s national security adviser, Mowaffak al-Rubaie, as saying, “This is the greatest day in the history of this country.”

Some 100,000 security personnel guarded polling places erected with reinforced windows to withstand the expected attacks from insurgents who for the last month pledged to assassinate voters and candidates. Security for the vote was so tight that the names of the actual candidates for the 275-person national assembly were not publicized until last week. Campaigning in the Sunni-dominated center of the country was severely limited, and voters only cast ballots for party slates, not individuals.

While terrorists did manage to kill two dozen people and wound another 71 yesterday, for the most part the attacks did not appear to dissuade Iraqis from electing their next government. Early estimates of the turnout yesterday suggest higher than expected numbers of registered voters went to the polls. The Independent Electoral Commission of Iraq estimated a 72% turnout in the polls yesterday. Osama bin Laden and his Iraq affiliate, Abu Musab al-Zarqawi, had told Iraqis to boycott the vote.

The votes will be counted over the next 10 days by the Independent Electoral Commission of Iraq, a body established by the Coalition Provisional Authority last year. The IEC is independent from the interim regime of Prime Minister Allawi. The United Nations and the European Union sent missions to observe the balloting.

In a complex process, the commission will determine the percentages of the assembly that will go to the competing lists of candidates. Because most of the slates have fielded candidates for most of the 275 places in the national assembly, the higher the placement on the winning slate, the better chance the individual candidate has for assuming office. Iraq also voted yesterday for candidates for the Kurdistan regional government and the provincial bodies that will oversee affairs in Iraq’s 18 provinces.

Once the composition of the assembly is determined, that body will go about negotiating a status of forces agreement with America and her coalition allies under which the 150,000 soldiers now in Iraq can stay there.

The new assembly elected yesterday will also begin drafting a permanent constitution and select the officials in the executive branch of the government.

Secretary of State Rice said she was optimistic the assembly, which will likely be heavily weighted to the Shiite slate of candidates, will reach out to less represented groups as it forms the new government and writes the constitution. “I’m quite certain that they will try to put together an assembly that brings Iraqis together, rather than splitting them apart; that they will then move to write a constitution,” Ms. Rice said on CBS yesterday. “The process of democracy going forward now will have its ups and downs, its twists and turns as they try to put together institutions that can bridge their differences. But they’ve made a very, very good start today.”

On CNN yesterday, the former exile leader Ahmad Chalabi thanked the American people for helping make the election possible. When asked about his rocky relationship with the Bush administration, Mr. Chalabi said lower-level contacts between him and the administration had already started. He said he was not bitter towards the White House.

At an African Union summit in Nigeria, the secretary-general of the U.N., Kofi Annan, praised the courage of Iraqi voters, saying they were voting for the future of their country. In recent months, Mr. Annan has criticized the American-led November offensive in Fallujah and cautioned that the security atmosphere was too risky for a nationwide election.

In the Middle East, a region the president has said he hoped would be inspired to hold elections by Iraq’s vote yesterday, the reaction was muted. The Egyptian president, Hosni Mubarak, called the unelected interim prime minister, Iyad Allawi, to congratulate him on the smooth vote. He said he hoped the election would “open the way for the restoration of calm and stability” in Iraq, according to the Associated Press.

In Jordan, a spokesman for the Hashemite monarchy, Asma Khodr, said, “We hope that holding elections in these very difficult conditions will help achieve stability in Iraq, reflect the will of all the Iraqi people, and help Iraq recover its sovereignty.” Last Thursday, King Abdullah warned that the election may result in the partition of Iraq.

Iran’s former president, Hashemi Rafsanjani, warned that America may try to rig the votes. While other Iranian leaders not only praised the vote but also allowed many Iraqis living in the country to vote as expatriates, Mr. Rafsanjani said America may not accept an Iraqi government that is “free and independent and that does not stand next to America and Israel.”

In Washington, Senator Kennedy, who delivered a speech Thursday comparing America’s presence in Iraq to the war he ended up opposing in Vietnam, said the presence of American troops was spurring the insurgency. “The best way to demonstrate to the Iraqi people that we have no long-term designs on their country is for the administration to withdraw some troops now,” his statement said.

The election in Iraq came nearly two years after American and allied forces launched a military operation against Saddam Hussein in March 2003, and just over a year after the December 2003 capture of Saddam.