Separately, fighting continued through the night in Baghdad's Al-Sadr City neighborhood. Fresh clashes between government forces and al-Sadr's Al-Mahdi Army were also reported in the city of Al-Nasiriyah.
Iraqi authorities say they have taken control of the Al-Hayaniyah district in Al-Basrah after several hours of fighting.
Interior Ministry spokesman Major General Abdel Karim Khalaf told AFP that the operation was now over "without any strong resistance."
Lieutenant General Mohan Furaiji told Reuters that anyone carrying weapons will be arrested.
A U.S. military statement said the operation was backed by British artillery and U.S. aircraft, which bombed "criminal rocket and mortar sites."
British military spokesman Major Tom Holloway earlier said the operation opened with a massive show of force by U.S. and British forces, who pounded a deserted area of Al-Hayaniyah. He said the bombardment aimed at giving a "demonstration of the firepower available if required."
There was no clear information about casualties.
But Salah al-Ubaidi, al-Sadr's spokesman in the city of Al-Najaf, south of Baghdad, said the humanitarian situation in Al-Hayaniyah was "tragic," adding that the wounded were prevented from going to hospitals.
The head of al-Sadr's office in Al-Basrah, Harith al-Idhari, said Al-Mahdi Army fighters were putting up no resistance.
Meanwhile in Baghdad, fighting continued after fierce clashes late on April 18 in the Al-Sadr City district, the cleric's power base in the capital. Reports say at least 12 people have been killed and more than 80 wounded.
One unidentified resident said the clashes led to the destruction of her house and the death of an elderly resident: "We have never seen anything like this and we will never see. They have been striking us all night long. Now, they destroyed our house and killed an elderly woman. We've never seen such a thing. Please, please find a solution. We can't stay like this forever."
U.S. military spokesman Lieutenant Colonel Steven Stover said U.S. troops were involved in sporadic clashes that continued today.
Reports say tensions have been increased by the construction of a wall in the district by U.S. and Iraqi forces.
Stover said the wall was needed to prevent rocket fire coming from Al-Sadr City and aimed at the heavy fortified Green Zone compound that houses Iraqi government buildings and embassies.
Clashes also erupted overnight between government forces and Al-Mahdi Army fighters in the southern city of Al-Nasiriyah.
District police chief Hassan Yassir said a curfew was imposed in Al-Nasiriyah and all the main roads linking the city with other provinces closed.
Al-Basrah was the scene of intense fighting about three weeks ago, after Iraqi forces made an attempt to disarm militias in the city. The fighting spread to various parts of Iraq, including in Baghdad's Al-Sadr City, killing hundreds of people. The militias were not disarmed, but promised to take their weapons off the streets.