The $592 million, 104-acre compound that was dedicated in Baghdad's fortified Green Zone on Monday is meant to symbolize a long-term commitment to Iraq.
As US forces pull back, Iran is expected to widen its influence in Iraq, despite the two countries' history of war and mistrust.
Control of roads and rural areas vexes coalition effort.
US forces may stay in the volatile northern city beyond the June deadline for Americans to pull back to bases.
Many Iraqis say passage of the US-Iraqi security pact ushers in a new era in which US military power will be replaced by Iraqi political power.
Hajji Hammadi, a senior member of Al Qaeda in Iraq, was believed by US military officials to have been responsible for the abduction and murder of US Army Staff Sgt. Matt Maupin in 2004.
Despite attack, Dulaim vows to bar Al Qaeda in Iraq, which it ousted from the town last year.
The American military is handing over control of projects in the troubled province ahead of a US-Iraqi security pact that could reduce the US footprint next year.