More than 5,000 US-led forces are sweeping through lawless hotspots in an area south of Baghdad known as Iraq's "triangle of death".
Direct combat is not expected in Operation Plymouth Rock
US, Iraqi and British troops have been conducting house-to-house searches and setting up vehicle checkpoints.
Renewed violence has hit Iraq's Sunni Muslim heartland in recent weeks.
The upsurge in attacks follows the large assault on Falluja earlier this month, which aimed to stabilise the country before elections in January.
The joint operation, dubbed "Plymouth Rock", began in the village of Jabella, 80km (50 miles) south of the Iraqi capital on Tuesday, where 32 people were arrested.
In other raids in Iskandariya and Latifiya, another 45 suspects were reportedly arrested.
These restive Sunni towns, along with neighbouring Yusufiya and Mahmudiya, are known for deadly attacks by Sunni Muslim rebels against US-led forces in recent months.
Correspondents say that unlike the assault on Falluja, there has been little combat, just a series of raids to wrest control from local gunmen.
"It's characterised by precision, patience and persistence - the keys to a successful counter-insurgency," said US spokesman Capt David Nevers.
Gunmen killed an Iraqi National Guard soldier travelling by taxi to his base near Mahmoudiya early on Wednesday.
British troops have been brought in to "squeeze militants attempting to run the 'rat lines' between northern Babil and Baghdad and al-Anbar provinces," a US statement said.
On Tuesday night, insurgents fired two rockets at the camp occupied by troops from the Black Watch Regiment south-west of Baghdad, but caused no damage or casualties, British officials said.
Capt Nevers said the military believed that "some fighters from Falluja skirted away and came down to our area to, among other reasons, take a little bit of pressure off of Falluja".
In other developments:
- An audiotape said to be recorded by Abu Musab al-Zarqawi lashed out at Muslim scholars for not speaking out against US actions in Iraq and Afghanistan.
- Gunmen attacked a lorry in western Baghdad, killing its Kurdish driver, police said.
- A suicide car bomb attack in the same area left three people dead. A person filming the explosion was arrested, police said.
- Insurgents attacked Iraqi National
Guard forces in the northern city of Kirkuk, killing a soldier and a civilian.