US and Iraqi forces have been battling Moqtada al-Sadr's Mahdi Army there since March 25.
Petraeus and Crocker shared the stage with presidential hopefuls, who all had much at stake.
Iraq's oil minister says the assault helped curb oil smuggling.
While the Sunni heartland has largely turned against Al Qaeda in Iraq, insurgents are still doing battle in the 'wild' reaches of the province.
A week after a truce calmed clashes between Moqtada al-Sadr's militia and Iraqi forces, fighting resumed in his Baghdad stronghold Sunday.
Gen. David Petraeus and Ambassador Ryan Crocker will describe Iraq's fragile state this week on Capitol Hill.