"The world is hearing the voice of freedom from the center of the Middle East," Bush told reporters at the White House on Sunday, four hours after the polls closed. He did not take questions after his three-minute statement.
Bush praised the bravery of Iraqis who turned out to vote despite continuing violence and intimidation. Bush said voters "firmly rejected the antidemocratic ideology" of terrorists.
Iraqis defied threats of violence and calls for a boycott to cast ballots in their first free election in a half-century Sunday.
Insurgents struck polling stations with a string of suicide bombings and mortar volleys, killing at least 44 people, including nine suicide bombers.
"Some Iraqis were killed while exercising their rights as citizens," Bush said. He also mourned the loss of American andkilled Sunday.
Bush cautioned that the election will not end violence in Iraq, but said U.S. forces will continue training and helping Iraqis "so this rising democracy can eventually take responsibility for its own security."
In a statement Sunday, Sen. Edward M. Kennedy, D-Mass, said Bush "must look beyond the election."
"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" and negotiate further withdrawals, Kennedy added.
Earlier Sunday, Secretary of State Condoleezza Rice said Iraqi will now work to reduce ethnic or sectarian differences, and the United States will discuss the continued need for outside security forces with the newly elected Iraqi government.
"We all recognize the Iraqis have a long road ahead of them," Rice said on CBS' "Face The Nation."
"The insurgency is not going to go away as a result of today," Rice added.
The election will give a lift to Rice as she makes her first trip as secretary of state later this week to Europe and the Mideast.
The successful results may help nudge the Europeans to do more in Iraq and help de-frost relations with the U.S., reports CBS News Correspondent Joie Chen.
Rice would not say whether U.S. forces will leave the country in great numbers after the vote, and Bush did not mention any U.S. military withdrawals.
So far, more than 1,400 U.S. troops and many thousands of Iraqis have lost their lives. The United States is spending more than $1 billion a week in Iraq.
Rice said the election went better than expected, but did not elaborate on U.S. predictions for turnout, violence or other measures.
In Iraq, officials said turnout among the 14 million eligible voters appeared higher than the 57 percent they had predicted. Complete voting results are not expected for days.
Polls were largely deserted all day in many cities of the Sunni Triangle. In Baghdad's mainly Sunni Arab area of Azamiyah, the neighborhood's four polling centers did not open at all, residents said.
A low Sunni turnout could undermine the new government and worsen tensions among the country's ethnic, religious and cultural groups.
"It is hard to say that something is legitimate when whole portions of the country can't vote and doesn't vote," Sen. John Kerry, D-Mass., said in a broadcast interview.
The Bush administration has a great deal riding on the election. Strong turnout and results that the world views as legitimate could speed the departure of American troops.
A stable Iraqi government could help mend alliances frayed by international opposition to the U.S.-led invasion, and Republicans on the ballot in 2006 and 2008 also would be relieved. Success could also buttress Bush's long-term goal to promote democracy across the Middle East, where family dynasties and authoritarian rulers outnumber democracies.
Problems with the election could complicate Bush's foreign policy aims, as well as the success of costly items on his second-term domestic agenda, such as partially privatizing Social Security.
Iraq's Shiite majority was widely expected to dominate the government that emerges from Sunday's elections, and some of the highest initial turnout reports came from overwhelmingly Shiite areas.
Even with lower turnout among Sunni Arabs, the government can be representative of all Iraqis, Rice said. She also downplayed concerns that a Shiite-dominated government will morph into a theocracy.
"I'm sure that they will have a healthy debate about the role of Islam, about the role of religion in that society," Rice said in a broadcast interview.