U.S. and Iraqi security forces swept through an area near the Syrian border to root out foreign fighters Sunday, the second day of one of the largest military offensives since the U.S.-led invasion in 2003.

About 3,500 troops participated in the operation in the region in and around Qaim, which the military has dubbed Steel Curtain. This is the second time in about a month that U.S.-led troops have stormed the expansive desert area in a full-fledged assault intended to expose fighters linked to the insurgent group al Qaeda in Iraq.

The offensive began Saturday, with troops battling insurgents in Husaybah, essentially a suburb of Qaim, about 200 miles northwest of the Iraqi capital.

"The combined force is clearing the city, house by house, as the al Qaeda in Iraq-led insurgents continue to plant improvised explosive devices throughout the city and fire on Marines and Iraqi army soldiers from homes, schools and mosques," the Marines said in a statement.

Iraqi officials have acknowledged that they are failing to stop fighters from crossing into the country from Syria. The fighters traverse the Euphrates River valley region, dispersing weapons and explosives, and then move on to the cities of Ramadi, Baghdad and Mosul. The officials have repeatedly criticized the Syrian government for not doing more to control their side of the border, while also noting that Iraqi troops are not yet adequately trained to do the job without U.S. support.

By Sunday afternoon, U.S. and Iraqi forces controlled seven of 11 neighborhoods in Qaim, witnesses said. At 10 a.m., the U.S. forces raided the neighborhoods and searched the houses, digging up gardens in search of contraband. The soldiers found weapons caches and papers linked to the al Qaeda insurgency, the witnesses said.

"I think the town will be cleansed within three to four days," said Iraqi army Capt. Arkan Hussein. "Only small pockets of the fighters remained."

The U.S. troops used loudspeakers to urge residents remaining in the city to help the joint forces by giving information on insurgents' hideouts and potential car bombs.

Mohammed Azzawi, a physician at the Qaim hospital, said five civilians had been killed and nine wounded since the assault began. He said 13 civilians were missing and presumed trapped under wreckage.

The Marines said there had been no reports of civilian casualties. "Marines can confirm 17 insurgents have been killed since the operation began" on Saturday, the Americans said in a statement. "Many more are suspected of being killed, but Coalition forces haven't been able to confirm those numbers yet."

A statement reportedly from the al Qaeda group that was posted on a mosque in Haditha claimed victory in the now two-day battle. "The heroes of al Qaeda are fighting and got what they wanted from the worshipers of the cross and the worshipers of the graves," the statement said. "Worshipers of the graves" refers to Shiite Muslims.

The group said nine of its fighters were killed during the offensive and that four were foreigners.

Al Qaeda in Iraq is led by Abu Musab Zarqawi, a Jordanian who has been behind some of the deadliest attacks, Iraqi and American intelligence officers have said.

"Many of the attacks are done by remnants of the last regime and former Baathists in cooperation with the Zarqawi people," the chief of Iraq's intelligence service, Hussain Ali Kamal, said recently. "We can't totally control these operatives because the Iraqi forces are not qualified enough yet."

In the desert east of Qaim, 31 families set up tents while the sound of gunfire rang out from their city.

"We don't have relatives in other cities, so we have to stay here," said Thaer Hamid, 47, who fled Qaim on Saturday. "We also do not have enough money to go to hotels like other people."

In another tent, Saadi Mohammed Janabi, 39, huddled with his family. He said that U.S. troops had provided the people in the camp water tanks for drinking and washing.

Special correspondent Bassam Sebti contributed to this report.

Marine Sgt. James H. Harrison looks over a rooftop during operations in Husaybah, Iraq, near Syria.