Hundreds of US troops have been diverted from Falluja to Mosul, as violence continues to spread to other areas of Iraq.
Insurgents are reportedly in control of some areas of Mosul
After four days of fighting, insurgents are reported to be in control of parts of Mosul, where residents say gunmen are roaming the streets.
Meanwhile, in Ramadi, clashes continued between troops and rebels.
And a US soldier has been killed and three others injured in an attack on a military base near Baghdad.
A ban on civilian air traffic over Baghdad has been extended, which closes the airport indefinitely to commercial flights.
The American army is reported to have shifted 500 soldiers from the US-led assault on Falluja, and sent them to Mosul.
Residents say rebels are patrolling parts of the city, after storming and looting several police stations on Thursday.
But the US military said Mosul was calmer on Saturday, with only sporadic fighting in some areas. It said three of five bridges that span the River Tigris had reopened and a curfew had been lifted.
Brig Gen Carter Ham, commander of American forces in Mosul, said US forces had expected "some reaction" in the city in response to the operation in Falluja.
But he told US news network CNN he doubted the militants had gone to Mosul having escaped from Falluja.
Most "were from the northern part of Iraq, in and around Mosul and the Tigris river valley that's south of the city," he said.
The Baghdad government sent reinforcements to Mosul after Thursday's attacks on the police stations. The US military said it had launched air strikes the same night after a request by the city's governor.
Mosul has seen a spate of suicide car bombings against Iraqi and US forces in recent weeks.