A military spokesman said US troops had launched ground and air strikes on Thursday against "enemy targets" as part of Operation Iron Hammer, launched on Wednesday.
On Wednesday, a Spectre gunship destroyed a Baghdad warehouse which the US military said was a planning centre for attacks on its forces.
Two Iraqis were killed in a helicopter strike on a van which US forces said had been used to launch mortars.
In the US, the general in charge of US forces said about 5000 "dangerous" loyalists of ousted dictator Saddam Hussein are fighting the US-led occupation in Iraq but they can be overcome.
General John Abizaid, head of the Central Command, which runs operations in Iraq and Afghanistan, said the Saddam loyalists are well-armed, well-financed and have "a brutal and determined" leadership.
He told a media conference at the command headquarters in Tampa, Florida: "The clear and most dangerous enemy to us at the present time are the former regime loyalists."
"The clear and most dangerous enemy to us at the present time are the former regime loyalists"
General John Abizaid,
head of Central Command
Abizaid said followers of the former ruling Baathist party operate mainly around Baghdad and the northern cities of Falluja, Tikrit, Mosul and Kirkuk. Their main weapons are "improvised explosive devices," mortars, rocket-propelled grenades and sometimes small arms.
New Italian troops
Meanwhile, Italy sent fresh troops to Iraq just one day after a deadly bomb attack on the Italian base in the southern city of Nasiriya.
An explosives-laden truck was
driven into the building
Eighteen Italians, two of them civilians and nine Iraqi civilians were killed in what Italy's Deputy Prime Minister Gianfranco Fini called "our September 11".
Making good on pledges to help Iraq emerge from postwar chaos, 50 Carabinieri paratroopers left central Italy on Thursday to reinforce a contingent depleted and demoralised by Wednesday's blast.
The bodies of the dead troops are due back in Italy as soon as Saturday.
Defence Minister Antonio Martino visited the blast site in Nasiriya and blamed it on the "same people" who had carried out the 2001 attacks on the United States.
The Italian cabinet ruled on Thursday that the 2300-strong Italian contingent in Iraq would stay put.