A dawn assault with rocket-propelled grenades on a police station in the mainly Sunni district of Adhamiya on Saturday killed at least three officers - a day after Iraq's US-backed National Guard raided a historic mosque.
US tanks and helicopters helped beat off fighters after a three-hour battle near the Abu Hanifa mosque, where four worshippers were killed and 17 arrested on Friday.
Elsewhere in Baghdad, a US soldier was killed and nine wounded when their patrol was caught in an ambush, the US military said.
Also in the capital, armed men assassinated a senior adviser to Iraq's ministry of public works along with three of her employees in an attack on their car on Saturday, a ministry spokesman said.
Jasim Muhammad said Amal Abd al-Hamid al-Mamalji was killed with her driver, secretary and a security guard. The spokesman said the gunmen blocked Mamalji's car as she drove to work and opened fire.
Separately, in the western Amriya district, fighters in cars opened fire on an Iraqi National Guard unit. A guard at the scene said seven of the assailants were killed and seven passers-by wounded.
On Saturday US and Iraqi forces
battled fighters in Adhamiya
An all-out offensive by more than 10,000 US troops on the Sunni city of Falluja, just west of Baghdad, over the past two weeks has killed, by US estimates, about 1200 fighters.
Intended to quell fighters before an election due in late January, it has been accompanied by scattered violence throughout the Sunni heartlands north and west of the capital.
US official backtracks
A senior US general, backtracking somewhat on confidence expressed by other officers, acknowledged it was "too early to say ... that the backbone of the insurgency is broken".
Lieutenant-General Lance Smith, deputy US commander in the region that includes Iraq, added that his command may ask for 3000 to 5000 more troops. Confirming plans outlined some weeks ago, he said this would be mainly by delaying the scheduled departure of some soldiers, to improve election security.
On Thursday, Lieutenant-General John Sattler, commander of the 1st Marine Expeditionary Force at Falluja, had said he felt the all-out assault on the city had "broken the back of the insurgency".
US troops raided and searched
homes in Ramadi
Meanwhile, US forces have begun restoring basic services and clearing Falluja of explosives but have set no date for civilians to return to the city, an officer said on Saturday.
"This will be driven by events, not dates. We have to restore basic services such as water and electricity first," Major Francis Piccoli said. "We are also going from house to house to clear out any insurgents and weapons."
The International Committee of the Red Cross has criticised the "utter contempt" for humanity shown by all sides in Iraq amid the fierce fighting for control of Falluja.
Violence in north
In Ramadi, the scene of frequent clashes just west of Falluja, US forces sealed off roads into the city early on Saturday and called on people through loudspeakers to hand over "terrorists".
Helicopters flew overhead and Americans blocked access in or out of the majority Sunni city as troops searched buildings south of the centre.
Nine Iraqi soldiers were found
beheaded in strife-torn Mosul
In Mosul, nine Iraqi soldiers were feared executed on Saturday as US and Iraqi troops fought fighters in the city.
Senior Iraqi and US military sources said they probably belonged to an Iraqi army unit that had joined US troops for a massive onslaught against fighters in the country's third-largest city.
In another development, a Polish woman freed by kidnappers in Iraq and flown to Warsaw said she was treated well, raising hopes for other foreign captives after a week in which the only other woman held captive, British aid worker Margaret Hassan, was thought to have been killed.