US-led forces say they have killed 26 militants in overnight operations in the Sadr City area of Baghdad in which four vehicles were destroyed.
A number of houses were damaged in the operation
Troops also detained 17 militants in pre-dawn raids on the area, a Shia stronghold, the US military said.
But Iraqi hospital and police officials put the death toll at eight and said civilians were killed in their homes.
The raids are the latest in a series of US offensives against militants accused of smuggling weapons from Iran.
Tehran has consistently denied US accusations that it is helping militant groups in Iraq.
Iraqi Prime Minister Nouri Maliki criticised the raids on Sadr City, saying his government strongly opposed operations carried out by US-led forces without its permission.
In another development, the US military denied reports from Thursday that 20 headless bodies had been found south of Baghdad and suggested it had been misinformation spread by insurgents.
A US statement said troops had met "significant" resistance during the raids from militant small-arms fire and rocket-propelled grenades, as well as from roadside explosive devices.
Troops travelling in armoured vehicles had "used proper escalation of force rules to engage four civilian vehicles", the statement said, adding: "It is believed that the suspected terrorists have close ties to Iranian terror networks."
US military spokesman Lt Col Christopher Garver insisted all of those killed had been "shooting at US troops at the time".
"It was an intense firefight," he said.
One resident told reporters that US helicopters had launched missiles at targets in the densely populated district, home to more than two million people.
Another described how "a big American convoy with tanks came and began to open fire on houses - bombarding them".
"What did we do? We didn't even retaliate - there was no resistance," Basheer Ahmed added.
The government is demanding an explanation for the raids which also involved Iraqi special forces under their command.
US soldiers have carried out a series of raids north of Baghdad
It said any Iraqi forces had to get permission from the government before participating.
This will bring back memories of problems between the two sides last year, the BBC's Andrew North reports from Baghdad.
Mr Maliki had intervened to stop several US operations during a drive to restore security to Baghdad.
American commanders say interference from the Shia-led government was one reason the plan failed and it was over Sadr City that they most strongly disagreed.
But Sunnis, our correspondent adds, are likely to see this new move by the government as further evidence of what they say is its bias towards the Shia community.
US-led troops have also attacked what they call insurgent strongholds linked to al-Qaeda around the capital in the last few weeks.
US commanders believe these so-called "belt areas" are where many of the car bombs set off in the capital are made.