Four militiamen loyal to Iraq's radical Shia cleric, Moqtada Sadr, have been killed in clashes with US forces in Baghdad overnight, Iraqi officials say.
Moqtada Sadr's supporters say they came under fire
It is the first such fighting since a rebellion by supporters of the cleric ended more than a year ago.
The US military confirmed it had fought "anti-Iraqi forces" in eastern Baghdad.
Meanwhile, at least nine people have been killed in a bomb attack on police in Baghdad, while two died in a market bomb in Hilla, officials said.
In another attack, at least six people were killed by a bomb at a Shia mosque in Musayyib, some 60 km (40 miles) south of Baghdad, on Sunday.
Iraqi police told the BBC that the blast happened as people were arriving at a mosque for prayers.
'We were attacked'
The overnight clashes in Baghdad broke out when American troops went into the Sadr City district in the east of the city to try to arrest members of Mr Sadr's militia, the Mehdi army, according to Iraqi police.
A US spokesman would not confirm the nature of the operation, but said US forces came under attack.
"There were a series of engagements," starting shortly before 0100 (2100 GMT Saturday) and lasting until about 0230, he told the AFP news agency.
"It appears we were going out to conduct an operation with the Iraqi army who had thrown a cordon around an area they wanted to search. It looks like they were attacked," he added.
He said no US soldiers were hurt.
A spokesman for Mr Sadr in Baghdad told a different version of events.
"Several armoured vehicles arrived in three areas of Sadr City at about 0100. American soldiers dismounted and opened fire at random," he said.
"People came out of their homes to see what was going on and four were killed and 10 injured, all of them civilians."
The Mehdi army, based in southern Iraq, led two uprisings last year against US forces.
The confrontation was settled when Mr Sadr agreed to enter the political process, and the militia handed over its heavy weaponry in a cash-for-weapons programme.
Rescue workers remove a body after a bomb in Baghdad
But the BBC's Caroline Hawley in Baghdad says the new fighting comes at a time of tension in southern Iraq between British troops and Mr Sadr's followers.
UK forces last week arrested two Mehdi army commanders, and later stormed a police station in Basra after two British soldiers were arrested and handed to the militia.
Commandos under fire
In Sunday's bomb attack in Baghdad, police say a suicide bomber drove into a convoy of Iraqi special forces from the elite Wolf Brigade.
At least five of the nine dead were reported to be police commandos.
In the town of Hilla, south of Baghdad, a bomb on a bicycle blew up in a busy marketplace, killing at least two people, medical officials said.
Police quoted by Reuters news agency said a bomber cycled into the market before detonating his explosives.
One report said a stall selling music was the target of the attack.