Updated

Helicopter gunships and fighter jets streaked across the desert sky Saturday as American and Iraqi forces battled insurgents near the Syrian border, killing at least 50 militants in two massive offensives to stanch the flow of foreign fighters from Iraq's western neighbor.

The U.S. military reported the deaths of two American soldiers, killed north of Baghdad during an attack as they were taking a captive to jail.

Intelligence officials believe Iraq's western Anbar province is the main entry point used by extremist groups, including Abu Musab al-Zarqawi's (search) Al Qaeda in Iraq, to smuggle in foreign fighters. Syria is under intense pressure from Washington and Baghdad to tighten control of its porous 380-mile border with Iraq.

On Thursday, a U.S. general called Syria's border the "worst problem" in terms of stemming the flow of foreign fighters.

The next day, about 1,000 U.S. and Iraqi forces backed by battle tanks launched an offensive the desert wastes around Karabilah and Qaim. The operation entered its second day Saturday in Karabilah (search), a dusty town about 200 miles west of Baghdad that is considered an insurgent hub.

About 50 insurgents have been killed since the operation began, Marine Capt. Jeffrey Pool (search) said from Ramadi, the provincial capital. Three U.S. troops have been wounded and about 100 insurgents have been captured, the military said.

Dozens of buildings in Karabilah were destroyed after airstrikes and shelling, according to an Associated Press reporter at the scene.

"The goal is not to seize territory," said Marine Col. Stephen Davis, of New Rochelle, N.Y. "This is about going in and finding the insurgents."

Karabilah's streets were empty, and the military said about 100 people fled the town. At one home, a family gathered on their porch, hanging a white flag from the roof to signal U.S. jets not to bomb their home.

Troops searching the town found four Iraqi hostages beaten, handcuffed and chained to a wall in a bunker, Davis said.

Some of the men were believed to be Iraqi border guards. Troops searching the bunker found nooses, electrical wire and a bathtub filled with water for electric shocks and mock drownings, Davis said.

Later, Marines and Iraqi soldiers took fire outside a mosque and a small band of insurgents fled inside, Pool said. Three militants were killed.

The U.S. military also reported incidents of insurgents breaking into homes and using families as human shields, resulting in injuries to 10 civilians.

U.S. and Iraqi forces also found a bomb-making factory in the town, Pool said. It contained blasting caps, cell phones and other materials to make roadside and car bombs, he said. Troops also found sniper rifles, ammunition and a mortar system.

A nearby schoolhouse believed to be used for training terrorists had instructions for making roadside bombs written on a chalkboard, Davis said.

A second offensive of similar size was launched Saturday, targeting the marshy shores of a lake north of Baghdad. About 1,000 Marines and Iraqi troops, backed by fighter jets and tanks, took part.

The second offensive seeks insurgent training camps and weapons caches in the Lake Tharthar area, 53 miles northwest of Baghdad.

On March 23, U.S. and Iraqi forces killed about 85 militants at a suspected training camp along Lake Tharthar and discovered booby-trapped cars and training documents. Among the insurgents captured then were Iraqis, Filipinos, Algerians, Moroccans, Afghans and Arabs from neighboring countries, officials said.

But the western region has been flush with militant fighters in recent weeks.

Insurgents in the area killed 21 people, believed to be missing Iraqi soldiers, whose bodies were found June 10. A day after that discovery, U.S. Marines carried out airstrikes that killed about 40 insurgents on the outskirts of Karabilah.

Iraqi troops did not participate in earlier offensives in the area. This time, they fought alongside the Americans and used their language skills and local knowledge to spot foreign fighters, said Col. Bob Chase, chief of operations for the Second Marine Division.

Separately, the U.S. military said Saturday that two soldiers were killed and one was wounded after fighting with insurgents late Friday while transporting a detainee near Buhriz, about 35 miles north of Baghdad. A civilian and the detainee also were killed.

At least 1,719 members of the U.S. military have died since the Iraq war began in March 2003, according to an Associated Press count.

In other violence Saturday, insurgents killed at least four people in Baghdad, including two Iraqi soldiers and a 10-year-old girl in separate incidents, hospital and police officials said. Twenty-one people — including an Iraqi journalist — were wounded in the suicide bombings and shootings.

Also, a farmer found seven corpses in a field in eastern Baghdad, police said. The men, wearing civilian clothes, were shot in the back of the head and had their hands bound.

The body of a Sunni tribal leader also was found Saturday outside Mahmoudiya, about 20 miles south of Baghdad. Sheikh Arkan Shaalan Jassim al-Edwan, who had been shot, was sprawled on a fallen roadside portrait of Saddam Hussein, police Lt. Adnan Abdullah said.

More than 1,100 people have been killed since Prime Minister Ibrahim al-Jaafari's Shiite-led government was announced April 28.