The leader of the Iraqi Front for National Dialogue, Salih al-Mutlaq, on Sunday denounced the massive US military offensive - code-named Operation Steel Curtain - being conducted in Husaiba, Karabla and al-Qaim - in western Iraq.
Al-Mutlaq, who is also a member of the committee that drafted the new constitution, accused the Americans and their Iraqi allies of mounting "a destructive and killing operation of secure cities and villages" on the "pretext that they hide and secure terrorists".
In Baghdad, Muhsin Abd al-Hamid, the head of the largest Sunni Arab political party, condemned "all military operations directed against civilian targets" because they "lead to the killing of innocent people and the destruction of towns and cities".
The US military launched the operation in western Iraq to root out what it says are foreign fighters and prevent the flow of men and materiel from Syria.
Some 3500 soldiers and marines, including 1000 Iraqi troops, are involved in the operation.
Scores of Iraqi families fled besieged towns on Sunday, waving white flags and hauling their belongings to escape a second day of the US offensive.
Residents of the area said by satellite phone that sounds of explosions diminished somewhat on Sunday, although bursts of automatic weapons fire could be heard throughout the day.
The residents said US forces used loudspeakers to instruct residents to leave on foot since vehicles would be fired upon.
Husaiba is a market town 320km
northwest of the Iraqi capital
"I left everything behind - my car, my house," said Ahmad Mukhlif, 35, a teacher who fled Husaiba early on Sunday with his wife and two children while carrying a white bed sheet tied to a stick.
"I don't care if my house is bombed or looted, as long as I have my kids and wife safe with me."
US forces said about 450 people had taken refuge in a vacant housing area in Husaiba under the control of Iraqi forces.
Others were believed to have fled to relatives in nearby towns and villages in Anbar province.
US officials insist Husaiba, a market town 320km northwest of Baghdad, is a stronghold of al-Qaida in Iraq and is an entry point for foreign fighters, weapons and ammunition from Syria.
Lying along the Euphrates River, the town is home to about 30,000 people.
The US military said its forces were
going house-to-house in Husaiba
On Sunday, US marines said that their air support struck at least 10 targets around the town on Sunday and that US forces were "clearing the city, house by house".
The US commander of the joint force, Colonel Stephen Davis, said his troops had moved "about halfway" through Husaiba.
Davis said at least 36 fighters were killed since the assault began on Saturday and another 200 men detained.
Davis would not comment on US and Iraqi government casualties but said the fighters were putting up a tough fight because "this area is near and dear" to them.
"This has been the first stop for foreign fighters, and this is strategic ground for them," he said by telephone.
Aljazeera reported the US army as saying two of its soldiers were injured during the assault on Husaiba.
Syria has denied helping fighters get into Iraq, and witnesses said Syrian border guards had stepped up surveillance on their side of the border since the assault on Husaiba began.
The US military said its troops found two weapons caches near Forward Operating Base Anaconda in Iraq.
The seizure yielded nearly 30 large-caliber artillery shells, more than a dozen rockets, five rocket-propelled grenade launchers, a mortar tube, a machine gun and small-arms ammunition, a military statement said.
An explosive ordnance disposal team collected the weapons and conducted a controlled detonation of the shells and rockets, it added.
Elsewhere, the US army says its snipers had killed eight suspected fighters on Sunday in separate incidents in Ramadi, capital of Anbar province.Three others were killed when they drove to the site of the first shooting and began firing "sporadically in all directions", the statement added.
The US statement said one of the fighters was shot dead when he was found allegedly planting a roadside bomb.
The other four were killed after trying to plant roadside bombs in other parts of the city, the statement said.
US helicopters and fighter jets
have been pounding Husaiba
In Baghdad, two people were killed and nine wounded when a car bomb exploded near a tunnel, police Captain Qasim Husain said.
The US military said four US soldiers were killed and three others wounded in sporadic attacks in Iraq.
US plane shot down
In a separate incident, al-Ishrin brigades, the armed wing of a group calling itself the Islamic resistance in Iraq, have displayed video footage on a website in which al-Zalazil brigade, an affiliate of al-Ishrin brigades, depicts an unmanned US military aircraft being shot down in Diyala province, south of Baghdad.
The group said US forces had been searching for the downed aircraft but were unable to locate it since they are in possession of the aircraft and later showed more footage of the wreckage.
The information on the website could not be independently verified.