President Bush hailed Thursday's voting in Iraq as "a major milestone" in establishing a democratic ally for the United States in the Middle East and moving toward withdrawal of American troops.

The appearance of a buoyant Bush in the Oval Office alongside six smiling young Iraqis displaying purple-stained fingers was an attempt to capitalize on any positive news in Iraq. The parliamentary elections carried high stakes for a White House confronted with increasing public and congressional dissatisfaction with the war.

Bush said, "There's a lot of joy, as far as I'm concerned" about the voting, adding that he was happy with the turnout even without final tabulations.

"We're certain that the turnout was significant and that the violence was down," Bush said, standing in the Oval Office before a roaring fire.

The U.S. commander in Iraq, Gen. George Casey, said there was less violence than during the previous election in October, and more voter participation, including a substantial increase in voting in the predominantly Sunni Anbar province, a hotbed of the insurgency. But he predicted tough and divisive times ahead for the new government.

"We should expect the insurgency not to just go away, but to gradually reduce," said Casey, speaking via video to a town hall-style meeting of Defense Department workers in the Pentagon.

Defense Secretary Donald H. Rumsfeld declared, "This election constitutes a defeat for the enemies of the Iraqi people, the enemies of the legitimate Iraqi government. It constitutes a defeat to the people who have been doing the beheadings and conducting the suicide raids."

There was a strong turnout in Sunni Arab areas, reinforcing U.S. hopes of seeing a stable government and calming the insurgency enough to begin withdrawing some American troops next year. Sunnis had shunned voting last January. Delays in vote counting were expected.

Sen. Lindsey Graham, in Baghdad for the voting, said he was encouraged by what he saw but it was only a step toward building a stable democracy in Iraq, and more help is needed from the international community.

"Let's don't take this election to mean the problems in Iraq are solved — really in many ways they're just beginning," Graham, R-S.C., said Thursday in an interview with NBC's "Today" show.

"We've got a second chance on life here after this election," he said. "Look at this election as a chance to re-engage and learn from our mistakes."

Bush had a more upbeat take.

"This is a major step forward in achieving our objective, which is ... having a democratic Iraq, a country able to sustain itself and defend itself, a country that will be an ally in the war on terror and a country that will set such a powerful example to others in the region, whether they live in Iran or Syria, for example," he said.

He congratulated Iraqis for "refusing to be cowed into not voting" and assured them the United States would stick with the mission there "until we complete this job."

"They don't have to worry. We're doing the right thing," he said.

A day earlier, Bush warned that the elections would be "followed by days of uncertainty," with final results perhaps not available until early January and violence not expected to wane.

The Iraqis who came to the White House to stand by the president's side voted in the United States; the purple ink on their fingers has become the standard mark in Iraq to ensure against multiple voting.

Also in Baghdad, Sen. Joseph Biden, D-Del., said the hard part for the Iraqis would come after the vote — forming a government and possibly amending the constitution.

"The bottom line is they still need us here," Biden told CBS' "The Early Show." "But the key to this is not a military solution. It's a political solution."

Iraqis need to write a constitution that the nation's disparate groups can accept. If they don't, Biden said, "all the troops in America will not be able to hold this country together."