Several thousand US and Iraqi troops have met sporadic resistance during an offensive against al-Qaeda militants near Iraq's Syrian border
US troops have dealt with militant strongpoints and roadside bombs
Some 2,500 American marines and other troops, as well as about 1,000 Iraqi government soldiers, are involved near Husayba, the US military said.
It is the first time Iraqi troops have been used on a major scale in the western Anbar province, it added.
There have been no reports of military or civilian casualties.
Operation Steel Curtain comes after two offensives near the Syrian border last month.
"The force is moving through the city to restore security along the border," a statement said.
"The Iraqi and US forces have encountered sporadic resistance - mostly small arms fire and improvised explosive devices - from al-Qaeda in Iraq-led insurgents throughout the city."
At least nine strikes were ordered against what the US military described as "strongpoints" which had been firing on troops.
At least 400 civilians who have fled the fighting are being sheltered in an abandoned housing estate.
Its aim is to "restore security along the Iraqi-Syrian border and destroy the al-Qaeda in Iraq terrorist network operating throughout Husayba", the US military said in its statement.
Iraqi units have included scouts tasked with identifying militant strongpoints and unexploded bombs.
The area's population is predominantly Sunni Muslim.
Sunni political parties in Baghdad have criticised the operation, saying that innocent people would be the victims, said the BBC's correspondent Jim Muir from Baghdad.
They have taken issue with a recent statement from the Iraqi defence minister, who threatened to bring down the houses of militants on their heads.
Troops, the US military added, are tasked with both finding insurgents and locating their "safe houses" ahead of the Iraqi parliamentary election on 15 December.
Steel Curtain also "marks the first large-scale employment of multiple battalion-sized units of Iraqi Army forces in combined operations" with US-led forces.
The area around Husayba, located near the border town of Qaim and is about 320km (200 miles) west of Baghdad, is used by al-Qaeda in Iraq to smuggle in foreign fighters, money and equipment, the US military believes.
US troops have used Iraqi scouts to hunt down militants
"They do not bring battalions - they bring the leadership, the financial man, the demolition expert," Marine Col Stephen Davis told AFP news agency.
Al-Qaeda in Iraq is among Iraq's most feared militant organisations, having claimed responsibility for many of the country's bloodiest bombings and beheadings.
Its commander is said to be Jordanian militant Abu Musab al-Zarqawi.
October's two big operations, Iron Fist and River Gate, were aimed at ending al-Qaeda militants' "campaign of murder and intimidation" in the province.
Last week, US warplanes destroyed a building in Husayba, killing five leaders of the militant al-Qaeda group, according to military statements.
In another development, a prominent Sunni Muslim politician has been seriously injured in a shooting in Baghdad.
Fakhri al-Qaisi, a spokesman for the Iraqi National Dialogue Council was shot several times when the car he was travelling in was ambushed in the mainly Sunni neighbourhood of Ghazaliya in the west of the city.