Isolated pockets of fighting occurred mainly in the west and southwest of Mosul on Monday, the US military said.
Two US soldiers were wounded in a car bomb attack on a convoy on the highway leading west from the city.
"I expect the next few days will bring some hard fighting," US northern commander Brigadier General Carter Ham said in a statement. "The situation in Mosul is tense, but certainly not desperate."
Iraqi fighters captured several police stations last week and some police stripped off their uniforms to join them.
US troops fought for two hours to retake one station on Sunday.
Most stations had been recaptured and many police had returned to duty, Ham said.
"There are a few stations which remain vacant - generally those which were heavily looted or burned," he said.
"Multinational forces and Iraqi forces patrol to ensure insurgents do not occupy these few stations. No stations are occupied or controlled by insurgents. I expect sufficient police will be on hand in a few days to control all the stations."
US and Iraqi troops had raided Iraqi hideouts and "had some success", he said, but gave no details.
Violence flared in Mosul after 10,000 US and 2000 Iraqi troops stormed Falluja, 50km west of the capital, last Monday to recapture the city from Iraqi control.
Iraqi fighters in Mosul have been
targeting Iraqi policemen
Iraq's interim government and its US backers said Falluja was the epicentre of anti-US activity in Iraq, from where most of the bombings, killings and kidnappings that have swept the country were masterminded.
But they also said many Iraqi fighters fled the city before the offensive, which the US military says has killed more than 1000 Iraqi fighters and 38 US soldiers.
Several Iraqi groups have condemned the offensive on Falluja, saying the US is indiscriminately bombing the city and needlessly harming civilians.