The coalition has the blessing of Iraq's Shia spiritual leader, Grand Ayatollah Ali al-Sistani, and is expected to become the biggest single force in the new 275-member national assembly.
A list headed by interim Prime Minister Iyad Allawi came in second, with about 18.4 percent in the partial count.
Highlighting the country's first free vote in five decades in his annual State of the Union speech, Bush said "the new political situation in Iraq opens a new phase of our work in that country."
"We will increasingly focus our efforts on helping prepare more capable Iraqi security forces, forces with skilled officers, and an effective command structure.
"As those forces become more self-reliant and take on greater security responsibilities, America and its coalition partners will increasingly be in a supporting role," he added.
Rebels murdered 12 Iraqi soldiers near the oil-rich northern city of Kirkuk late Wednesday.
On Thursday, one Iraqi was killed and four wounded as they drove to work at a US base at Baquba. Two civilians were also killed when a mortar attack fell short of a US position in Tall Afar, west of Mosul, the US military said.
Elsewhere north of Baghdad, three Iraqi soldiers were killed in a bomb attack in Yathrib. A soldier and a woman died when a bomb targeted an army convoy at Shorgat, while the body of a driver working for the US military was found in the Tuz region.
A civilian was killed by a roadside bomb near Abu Ghraib in western Baghdad, while a bomber died trying to blow up a vehicle on the main Baghdad airport road, said the US military.