Residents of the sprawling eastern Baghdad district which has been under vehicle curfew since March 28 reported sporadic firefights punctuated by mortar fire through the night and into the morning.
Around 70 people have been killed and scores wounded since fresh clashes broke out in Sadr City on Sunday.
Among those killed were three members of a family who were having breakfast when a mortar round smashed into their home.
The US military says it is chasing "criminals" firing rockets into Baghdad and the heavily-fortified Green Zone where the Iraqi government and US embassy are based.
Small arms fire
It said on Thursday that 13 "criminals" were killed in operations the previous 24 hours in Sadr City and northwest Shuala neighbourhood, another Mahdi Army stronghold.
In one incident, a combined US-Iraqi checkpoint was attacked from a nearby rooftop by small arms fire and troops retaliated, killing one of the attackers, a military statement said.
Another four fighters were killed when troops retaliated after they were attacked with rocket-propelled grenades at a checkpoint, while a air raid on Wednesday night killed four armed men after they attacked Iraqi troops.
At least 12 US soldiers have been killed in Baghdad since Sunday, most of them in Sadr City, according to an AFP tally based on American military statements.
George Bush, the US president, is scheduled to give a speech in Washington on Iraq and US troop levels at 11:30 am (1530 GMT) on Thursday, the White House said.
|An Iraqi man holds up shrapnel allegedly|
from a US missile in a wreckage of a building [AFP]
Currently, there are more than 150,000 US troops in Iraq. After the "surge" brigades brought in last year to boost numbers leave by July, the total will be around 140,000 troops.
General David Petraeus, the top US commander in Iraq, in two days of congressional testimony has recommended that a drawdown of US forces from Iraq be suspended indefinitely once the surge ends in July.
A defence official in Washington said Bush was expected to announce a return to shorter 12-month tours for troops in Iraq and Afghanistan, ending 15-month tours that have strained the force.
Fears of a resurgence in violence in Iraq are running deep after al-Sadr threatened on Tuesday to end the truce his feared Mahdi Army militia has been observing since August because of government attacks on his militiamen.
US commanders acknowledge that the ceasefire was one of the factors behind a sharp drop in violence across Iraq in the second half of last year.
Al-Sadr fighters began clashing with security forces across Shia regions of Iraq on March 25 after Nuri al-Maliki, the Iraqi prime minister, ordered a crackdown on militiamen in the southern city of Basra.