US and Iraqi troops have pushed further into the western Iraqi city of Ramadi.
Parts of Ramadi have been no-go areas fro US troops
Helicopter gunships provided air cover as troops and armoured vehicles pushed into the east of the city, one of the strongholds of the insurgency.
The operations are an effort to extend patrols into areas where militants have frequently carried out attacks, US officials say.
Also on Monday, at least four people were killed in a car bomb attack on an Iraqi army patrol in Baghdad.
At least eight people were injured, Iraqi police said.
Violence is continuing in Baghdad despite the introduction of stringent new security measures last week that have seen more than 40,000 Iraqi and US forces deployed in the city.
In other violence:
- In the town of Madain, south of Baghdad, gunmen enter a house in the early morning and kill three members of a family while they are still in bed
- In Karbala, in southern Iraq, a police lieutenant-colonel and his three bodyguards are killed when their convoy is ambushed.
Prime Minister Nuri Maliki said on Monday that Iraqi forces will take over security in the southern province of Muthanna next month.
British forces currently oversee a multi-national contingent in Muthanna, which includes Japanese and Australian troops.
It will be the first of the provinces, outside the relatively peaceful north, to come under full Iraqi control.
'No major assault'
On Sunday, the military set up outposts in southern areas of Ramadi as part of what it said was an operation to cut supply lines to insurgents.
US military officials have insisted that the move is not the beginning of a major assault on the city.
An eyewitness, reported by the Reuters news agency, said tanks were being used in the operations in Ramadi.
Shops were shuttered and many residents stayed at home, fearing a major US offensive, the agency reported.
Reports say that people in Ramadi have been leaving for some days. Reuters quotes one resident as saying that the water and electricity have been cut off in his area of the city.
Residents have not been urged to leave the city by US or Iraqi troops.
Ramadi, the capital of Anbar province, has become a key centre of the Iraqi insurgency. Much of it has been a no-go area for US troops. It has a population of about 400,000.
Kidnapped US soldiers
In another development, the White House spokesman Tony Snow has said that US-led forces were trying to find two US soldiers apparently captured by Iraqi insurgents on Friday in Yusufiya, south-west of Baghdad.
He said as yet, the administration had no news about them.
The soldiers were captured after an attack on checkpoint they were manning. Some witnesses say they were kidnapped by masked militants.
On Sunday, US military helicopters and divers combed rural area along the Euphrates River.
The Associated Press news agency has reported that Yusufiya residents have been offered $100,000 for information leading US forces to the abductors of the soldiers. This has been denied by the US military in Baghdad.