U.S. and Iraqi troops battled house to house and street to street in the border town of Husaybah on Monday in the third day of a campaign to clear out insurgents and stop the flow of foreign arms and fighters from Syria into Iraq, the U.S. military said.

Troops "continue to be attacked by small groups of terrorists," the military said, adding that there had been four incidents of insurgents assaulting U.S. Marines and Iraqi soldiers from inside mosques and one attack from inside a school.

The U.S. military reported Monday that a Marine was killed by small-arms fire Sunday -- the first U.S. fatality of the offensive, named Operation Steel Curtain -- and that nine U.S. service members had been injured. About 40 insurgents have been confirmed killed, the military statement said.

In separate violence on Monday, four U.S. soldiers died when a suicide car bomber attacked their checkpoint on a road south of Baghdad, and late Sunday a soldier was killed by a roadside bomb near the town of Dawr, about 85 miles north of Baghdad, the U.S. military said in statements.

Khaleel Dulaimi, an official with the Red Crescent Society, said 29 civilians had been killed in the border offensive. Dulaimi was interviewed at a refugee camp east of the city of Qaim, which is about 10 miles from Husaybah and has also been targeted in the offensive.

Majbil Ahmad Mihalawi, a Qaim official, said 76 houses and four schools had been destroyed and two mosques had been severely damaged in the city. Water, sewer and electric systems also suffered major damage, he said.

The U.S. military said in its statement that it knew of no civilian casualties.

"Terrorists are using sensitive and critical infrastructure as protection from Coalition and Iraqi Army counterattacks," the military said. Marines were using "proportionate force in responding to attacks" while respecting "the sanctity of the mosques," the statement said, adding that no airstrike had been conducted against any mosque.

Senior U.S. military officials said the offensive in western Iraq, centered around a border crossing with Syria about 200 miles west of Baghdad, had multiple aims -- most important among them reestablishing Iraqi control of the border and stopping the flow of foreign fighters, weapons and money into Iraq. Other goals include destroying al Qaeda safe houses in the area, killing or capturing the group's leaders and disrupting the organization's command-and-control capabilities in the desert of Anbar province.

"What we saw developing over time was that the terrorist and foreign fighters were using villages and towns in al Anbar as safe havens -- that's where they were stockpiling munitions, that's where they were involved in building their bombs, that's where they were conducting their training," Maj. Gen. Rick Lynch, a senior U.S. military spokesman in Baghdad, said in an interview.

U.S. warplanes conducted nine airstrikes on Saturday and 10 on Sunday "using precision-guided munitions to ensure destruction of the target while limiting collateral damage," according to a military statement. In the eight days preceding the offensive, U.S. airstrikes destroyed at least 11 safe houses in and around Husaybah, killing at least nine of al Qaeda's top local leaders and more than a dozen other members of the group, according to the U.S. military.

Elsewhere in Iraq, six people were killed and nine were wounded in a mortar attack on civilian houses near Iraq's Ministry of Youth and Sport in the Mustansiriya neighborhood of eastern Baghdad, according to Gen. Salman Shammari of the Baghdad police. And at least nine people, including six Iraqi policemen, were killed in a suicide car bombing in the Dora neighborhood of southern Baghdad, news services reported.

In another attack, three armed men entered an Internet cafe in the northern city of Mosul on Monday and assassinated Ahmed Hussein Maliki, the number two editor of Tall Afar Today newspaper, according to an employee of the paper, who asked not to be named because of security concerns. He said the paper recently moved its offices from Tall Afar to Mosul, 35 miles to the east, because of threats against the staff.

U.S. Marines and Iraqi soldiers prepare to enter a house near the Syrian border. A Marine died Sunday in the offensive, in its third day yesterday.