"The world saw long lines of Iraqi men and women voting in a free and fair election for the first time in their lives," Bush said in a statement Sunday. "The United States and our coalition partners can all take pride in our role in making that great day possible."
Parties have three days to lodge complaints, after which the results will be certified and seats in the new National Assembly distributed. Seats will generally be allocated according to the percentage of votes that each ticket won.
"I congratulate the Iraqi people for defying terrorist threats and setting their country on the path of democracy and freedom," Bush said. "And I congratulate every candidate who stood for election and those who will take office once the results are certified."
Lawmakers appearing on Sunday talk shows said a political give-and-take to form a coalition is expected now that election results show no Iraqi group won the votes needed to form a new government on its own.
"That's really part of that democracy that we're all so happy that they're moving toward," Senate Majority Leader Bill Frist (search), R-Tenn., said on "Fox News Sunday."
The State Department called the election "a positive and significant accomplishment" and encouraged Iraqis who were not elected to remain involved in the political process.
The slate of Shiite Muslims for the 275-member National Assembly received just under half of the votes cast in the Jan. 30 elections, the first since Saddam Hussein was ousted as president in 2003. A two-thirds majority of the assembly chooses the president and two vice presidents, which could push the Shiites to form a coalition with other political groups.
"They're brand new at this and it really depends on how they reach out," said Delaware Sen. Joseph Biden, senior Democrat on the Senate Foreign Relations Committee.
The candidate list dominated by Kurds came in second while the slate put together by Prime Minister Ayad Allawi finished third. Sunni Muslims, who generally stayed home during the elections and cast just 2 percent of votes, still must be involved in writing the constitution for the Iraqi system to have legitimacy, many lawmakers said.
"It's the outreach by the Shiite leaders and those who are elected to include the Sunnis in the process that will be most important," Senate Intelligence Chairman Pat Roberts, R-Kan., told CNN's "Late Edition."
Roberts said he is trying to remain optimistic the new government will have separation of religion and government so an Iranian-style theocracy does not emerge. But Sen. Jay Rockefeller of West Virginia, the top Democrat on the Intelligence Committee, said he worries that an "Islamic way of law" is a possibility.
"I'm not afraid of it, but it's on my mind," Rockefeller said.