The US forces killed 19 members of Shia cleric Moqtada Sadr's Mehdi Army after arresting two key aides in a midnight raid.
Eighteen were killed in one clash when US troops moved in after militiamen began setting up checkpoints in Sadr City, a Shia slum that is one of the strongholds of the firebrand cleric, the military said.
An AFP correspondent said one Sadr supporter was killed and another wounded during the raid, which involved 20 US military vehicles.
Another seven people were killed and eight others wounded when a bomb ripped through a crowded Baghdad marketplace, hospital workers said.
The police officer heading criminal investigations in Baqubah died in hospital on Sunday after being shot in the city centre, police said.
"An unknown person shot Lieutenant-Colonel Ali Hussein al-Azzaui in the middle of the city before taking flight," police Lieutenant Mohammed Thamer told AFP.
Three British soldiers were wounded when an explosive device was hurled at their vehicle in the southern Iraqi port city, a spokeswoman for Britain's ministry of defence said.
A British convoy also came under fire in the city but there were no casualties in this attack.
In a third incident, a home made device exploded as a British military convoy drove along the seafront road, again without causing casualties, a British officer at the scene said.
Two Iraqis were killed in gun battles between Sadr's followers and US-led forces in the centre of the holy city of Karbala, medical sources told AFP.
The fighting lasted about three hours after breaking out in the afternoon near the Al-Mokhayam mosque, close to a Sadr office.
Four Iraqis were killed and 12 others injured, including four children, in fresh fighting between US troops and Sadr's militiamen in Kufa, according to witnesses.
The clashes broke out at around 2:00 p.m. (1000 GMT) and lasted for about two hours, according to witnesses.
Columns of flame and smoke were seen coming from the pipeline in an area 40 kilometres south of the southern city of Basra.
The new Najaf governor appointed by the US-led coalition will join tribal and religious leaders in efforts to broker an end to a stand-off between coalition troops and Shia radicals in this holy city, a senior police officer said on Sunday.
Several people including an unspecified number of British nationals were wounded Sunday in a blast outside a Baghdad hotel on Sunday, the British Foreign Office said in London.
"One explosion has occurred outside the Four Seasons Hotel in Bagdad," a spokeswoman told AFP.
"Some people have been injured and this includes Britons. We are not aware of the seriousness of the injuries," she said.