Coalition forces have been drawn into a campaign against Shia militias
US troops have killed 15 Iraqi militants in clashes in Shia areas of Baghdad, the US military has said.
The fighting took place in areas of the city controlled by the Mehdi Army militia of Shia cleric Moqtada Sadr.
There has been fierce fighting in Baghdad and the southern city of Basra since the government's campaign against the Mehdi Army began last month.
The Iraqi army commander in Basra has said his forces are in "almost complete control" of the port city.
An Iraqi operation against Shia militias in Basra began last month and has spread to Baghdad and other Shia areas, drawing in US and UK forces.
Moqtada Sadr has threatened "open war" against the Iraqi government if it does not call off its campaign against the Mehdi Army.
In Baghdad, the US military said air and ground forces were involved in a series of clashes against militants that began late Tuesday.
"Along with our Iraqi security forces partners, we are targeting individual terrorists, criminal networks, and anyone involved in violent crimes against the Iraqi people," said US military spokesman Lt Col Steven Stover in Baghdad.
A US military statement also said that seven Iraqi policemen and 11 civilians were killed in Tuesday's suicide bombing near a police station in Jalawla, north of Baghdad in Diyala province.
In Basra, the Iraqi commander, General Mohan Furaiji, told the BBC his forces had nearly gained complete control of the city.
Iraqi forces in Basra seems to be gaining ground after a shaky start
He denied reports that he had given the leaders of Shia militias in the city 24 hours to give themselves up.
The US has sent 800 troops to Basra to help the Iraqi army, and UK and US special forces are launching raids to detain key figures in the militias.
The Iraqi campaign in Basra got off to a shaky start, but appears to be gaining ground with increased support from coalition forces, says the BBC's Patrick Howse in Baghdad.
The most influential of the militias in Basra is the Mehdi Army. There are also the Badr Brigades - linked to the political party, the Supreme Islamic Council of Iraq.
There are signs that the militias' hold on the city is weakening, says our correspondent.
There are reports of women dressing less conservatively, couples walking arm-in-arm and live music being played at weddings - all things that would have been impossible a few weeks ago, adds our correspondent.