The insurgents may have regrouped, says First Marine Division commander Maj Gen Richard Natonski, after US-led troops took over large parts of the city.
Other reports speak of heavy aerial bombardment, and a fresh attack on rebel-held areas in the south.
Eighteen US and five Iraqi troops had been killed so far, and another 69 Americans and 34 fighters were wounded, he added.
US military officials say around 600 insurgents have died.
Residents trapped in the battered city said they could smell the stench of decomposing bodies.