The raids took place around 4am in the villages of Owesap and Betra.
Some 150 Iraqi soldiers participated in the operation, Major Alayne Conway, spokeswoman for the army's 3rd Infantry Division, said.
By midday on Friday, there were no casualties on either side, she said.
"These are areas where we believe al-Qaida was staging attacks, and we also believe they have ties to the May 12th attack," Conway said.
Three US soldiers were kidnapped after their patrol was ambushed on May 12 near Mahmudiya, also south of Baghdad.
Four other Americans and an Iraqi interpreter were killed in the attack, and an al-Qaeda-linked group claimed responsibility.
Two soldiers remain missing, and the body of the third was found in the Euphrates River nearly two weeks later.
Iraqi police said eight al-Qaeda fighters were killed in a separate incident in a Shia village near Muqdadiya, north of Baghdad.
"Iraq is still under foreign occupation and Iraqis continue to die in great numbers"
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Shia townspeople, backed by police, drove the Sunni fighters out of the village and killed eight of them, police said.
Meanwhile, a top British commander in southern Iraq said attacks plunged 90 per cent across the country's south after the UK withdrew its troops from the city of Basra.
The presence of British forces in the centre of Basra, Iraq's second-largest city, was the single largest instigator of violence, Major-General Graham Binns said on Thursday on a visit to Baghdad's Green Zone.
About 500 British troops moved out of a former Saddam Hussein palace at Basra's heart in early September, joining some 4,500 at a garrison at an airport on the city's edge.
Also on Friday, Falah Hassan Shanshal, the head of the Iraqi parliament's "de-Baathification Committee", said a draft law that would allow former Saddam followers to hold government jobs is unconstitutional.
The new law was submitted to parliament this week. If approved, it would relax curbs on former Baath Party members - a key demand of the US and Sunni Arabs.
Among other things, Shanshal said the law might open government jobs to low-ranking Baath members who had still committed crimes and would trigger a backlash among Iraqis - especially Shias.
On the ground, violence continued in Iraq on Friday, with one civilian killed by a roadside bomb outside a motorcycle shop in central Baghdad, police said.
|The US military says violence levels in Baghdad|
have declined in recent months [Getty]
Four others were wounded by the blast and transferred to a nearby hospital, they said.
About an hour earlier, assailants opened fire on the same spot, wounding one civilian, police said.
The attacks took place near the Abdul-Qadir al-Gailani mosque, a Sunni shrine in central Baghdad's Sinak district, a mixed area.
The previous day, a suicide car bomber struck in the northern oil city of Kirkuk, killing seven people and wounding 20 more.
Brigadier-General Khatab Aref Abdallah, the chief of the police emergency unit in charge of the fight against al-Qaeda in Kirkuk province, was among the wounded.