US forces have taken up positions in the Iraqi capital, Baghdad, in the first visible sign that a new security plan is being implemented.
Children were among those hurt in Sunday's fighting in Sadr City
At least 4,000 US troops are being deployed in an attempt to reduce sectarian killings and kidnappings.
Fighting erupted overnight in Baghdad when US troops raided a mainly Shia district to make arrests.
Gunmen killed six Iraqi soldiers and wounded 15 in an attack on a checkpoint on Monday near the city of Baquba.
In other violence:
Gen John Abizaid, head of US Central Command, has said civil war may erupt if sectarian violence is not halted.
- A suicide bomber drove an explosives-laden truck into the police commandos' regional headquarters in Samarra, killing nine soldiers and injuring at least 10 civilians, police said
- The Associated Press reported that five people were killed when gunmen opened fire in a barber's shop - a profession increasingly targeted by some militants who believe shaving is contrary to Islamic law
- Six soldiers were killed and 15 wounded when their checkpoint in the restive city of Baquba was attacked
- Two policemen were shot dead in their car, in a drive-by shooting in Mosul
- Two bombs exploded in Baghdad's Palestine Street, a popular shopping area, injuring at least three people
The BBC's Paul Wood notes that this is the first time the generals are talking openly about the possibility of a civil war in Iraq.
Officially 1,500 people were killed in July but this is actually down on the 3,000 a month in May and June, our correspondent says.
While commanders in Baghdad see this as a sign of progress another interpretation is that there is now less scope for sectarian violence as so many people have fled their homes, he adds.
Twenty thousand people became internal refugees in the last 10 days of July alone, according to official figures.
Baghdad is increasingly becoming a patchwork of Shia and Sunni enclaves looking nervously out across barricades, our correspondent says.
Our correspondent says that while the Americans will not state publicly how many extra soldiers are coming to the capital it could be up to 7,000.
US troops from the 172nd Stryker Brigade Combat Team were seen patrolling predominantly Sunni areas of the west of the city on Sunday.
The brigade is named after the eight-wheeled Stryker armoured car, regarded as being better suited to urban terrain than conventional vehicles.
They have spent the past year in the northern city of Mosul, and the Pentagon recently extended their tour of duty by four months.
Gen George Casey, head of coalition troops in Iraq, said their deployment was vital to the strategy of defeating death squads and other insurgent groups.
"Our strategy is to remain on the offence. In co-ordination with the prime minister and leaders within the Iraqi security forces, we are modifying our operational concept," he said.
Correspondents say the deployment is being seen as an admission that a two-month-old security operation involving 50,000 mostly Iraqi troops around Baghdad had failed to curb the violence.
American and Iraqi government troops seeking to make arrests in the Sadr City area of Baghdad fought a gun battle with Shia militants on Sunday night.
Two militants were killed and 18 people were wounded, including civilians, Iraqi security sources said.