Move follows pressure from Muqtada al-Sadr, whose militia was blamed for the clashes.
He landed in Anbar province, once a Sunni Arab fighter stronghold but now seen by the US military as a success story.
|Bush met US soldiers at the al-Asad base
in Anbar during his visit on Monday [AFP]
Admiral William Fallon, the commander of US forces in the Middle East, and General David Petraeus, the US commander in Iraq, were also at the base to meet Bush.
His arrival coincided with a British military pullback from its base in the centre of the southern Iraqi city of Basra.
Their assessment of the conflict, along with a progress report the White House must hand legislators by September 15, is expected to determine the next phase of US military involvement in Iraq.
Amid a rising US death toll, currently estimated at 3,700, and growing calls from the Democratic Party for a troop withdrawal, Bush is under pressure to decide whether to give al-Maliki more time to find a political solution to the crisis.