US troops fighting al-Qaeda militants in the Iraqi city of Baquba now control about 60% of the city's western side, their commander says.
The US is counting on Iraqi forces to police the area eventually
Brig Gen Mick Bednarek said a big challenge for his 10,000 soldiers was securing areas once they were clear.
The situation inside the city, 60km (35 miles) north-east of Baghdad, could not be confirmed independently.
Earlier, another US military official said al-Qaeda fighters were being "enveloped into a kill sack".
As of Sunday, US forces had trapped between 50 and 100 insurgents and were "closing the noose", Gen Bednarek said.
"It's the hard-core fighters left - guys who will die for their cause, as misaligned as that is - and they want to kill as many US forces as they can," the US commander added.
Gen Bednarek predicted it would be weeks before Iraqi police and troops could secure the area.
According to his figures, US forces have killed between 60 and 100 fighters in the city and one American soldier has died in the fighting.
Baquba is the capital of Diyala Province and has long been a centre of Sunni Muslim resistance to coalition and Iraqi government forces.