The al-Hadba Party emerged from Saturday's vote as a serious challenge to the status quo in Iraq.
Polls open throughout most of the country for a provincial election that could shift the balance of power.
While President Bush traveled to Baghdad Sunday to hail progress, the war is far from over in places like Mosul where US and Iraqi forces still battle insurgents linked to Al Qaeda in Iraq.
Despite attack, Dulaim vows to bar Al Qaeda in Iraq, which it ousted from the town last year.
In another nod to the West, Syria also sent an ambassador to Iraq – the first in decades.
The U.S. military says that an increasingly capable Iraqi Army could assume primary combat responsibility by mid-2009.
Anbar Province is where 1 of every 3 US fatalities in Iraq occurred.
As the secular government eases its firm control over society, Islamic firms are increasingly cropping up.
Iraqi troops took the southern city without a shot being fired from Shiite cleric Moqtada al-Sadr's Mahdi Army.