The operation was the most sustained action by US and Iraqi troops in recent days.
Officials have said that more than 130 people have died there since Saturday.
US and Iraqi troops describe the street as riddled with "terrorist hideouts" and a hotbed of armed activity by foreign fighters linked to al-Qaeda.
US fighter jets and military helicopters hovered above the area where the battle was centred, witnesses and the US military said.
Skirmishes began in the early hours of Tuesday and by daylight had grown into a heated exchange of fire, forcing residents to avoid main roads.
In a separate statement, the Iraqi defence ministry said its forces had arrested 11 people, including seven Syrians from Haifa Street.
|Pakistanis burn a US flag in Peshawar in |
protests against Saddam's execution [AFP]
The statement did not clarify when the arrests were made.
It said two of the four other men arrested were al-Qaeda members picked up from Yusufiya, south of Baghdad.
The ministry said that eight hostages were also set free in Haifa Street.
The latest bout of fighting came as a new video showing the body of Saddam Hussein, the ousted president, shortly after his hanging appeared on the internet on Tuesday.
"They could have used this as their ticket to a new life, instead they use their freedom to slaughter each other"
P McFall, Atlanta, US
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The footage shows his head sharply twisted to one side and a gaping wound to his neck.
The 27-second footage, apparently taken with a mobile phone camera, is expected to trigger fresh outrage over the manner in which the former president was hanged and his body treated immediately after the execution.
The footage begins by showing a body on a stretcher covered in a white shroud and the camera moving upwards.
As the camera reaches the head, the shroud is pulled aside to reveal the bearded face of Saddam twisted sharply to his right with a wound just below his jaw on the left side.
A few red blotches are also seen on Saddam's left cheek.
Voices can be heard, apparently of those shooting the film secretly.
As the shroud is pulled back one voice is heard saying: "Hurry up, hurry up. I will count one to four."
Then another voice is heard saying: "Abu Ali, you take care of this."
The latest video follows one posted on the internet a day after the hanging on December 30, also shot on a phone camera, which showed Saddam at the gallows being taunted by guards moments before the trap-door opens.