A key member of a terrorist network led by Jordanian-born militant Abu Musab Zarqawi was among 19 people killed in U.S. airstrikes Saturday in the insurgent-held city of Fallujah, witnesses and hospital officials said Sunday.

Abu Ahmed Tabouki, a Saudi said to be Zarqawi's right-hand man in Fallujah, was killed at 10:30 p.m. Saturday. Witnesses said his body was found near a bombed-out house owned by Omar Hadeed, an Iraqi also linked to Zarqawi's organization, Monotheism and Jihad.

The U.S. military did not disclose the identities of insurgents targeted in the strikes, but one senior military official told reporters that the bombing campaign was "making inroads into killing the leadership and the emerging leadership" of Zarqawi's organization.

The attack killed 11 people, officials at Fallujah General Hospital said. Doctors said a 10-year-old was among the dead. Eight people were killed in a separate strike Saturday morning, hospital officials said.

Officials of the U.S.-led military coalition in Iraq said commanders took great care to avoid civilian casualties but did not dispute that attacks over the last two weeks had killed civilians.

Insurgents responded to the airstrikes with two nearly simultaneous suicide bombings Sunday morning near the headquarters of the Iraqi National Guard outside Fallujah. The U.S. military reported that two vehicles carrying explosives, a black BMW and a blue KIA pickup truck, were thwarted by a barrier system and that the blasts caused only minor injuries to U.S. and Iraqi forces. The two drivers were killed.

The U.S. bombing campaign in Fallujah appears to be aimed at weakening Zarqawi's grip on the city without sending in U.S. forces. U.S. troops have not operated in Fallujah since early May after the end of a three-week offensive ordered in response to the killing and mutilation of four American contractors.

U.S. intelligence officials say they believe Zarqawi is al Qaeda's point man in Iraq, and a $25 million reward has been offered for information leading to his capture. In addition to orchestrating attacks against U.S. and Iraqi forces, he was identified on videos as the man who beheaded two American contractors, Eugene "Jack" Armstrong, 52, and Jack Hensley, 48, last week.

The fate of Kenneth Bigley, 62, a Briton who was kidnapped with the two Americans, and several other Europeans remained uncertain, as did the fate of other foreign and Iraqi hostages.

Also Sunday, the U.S. military announced that a senior commander of the Iraqi National Guard was arrested Thursday "for having associations with known terrorists, for alleged ties to insurgents." In a statement, the military said the commander, Lt. Gen. Talib Abd Ghayib Lahibi, had been one of five nominees to serve as National Guard commander for Diyala province, northeast of Baghdad.

In addition, a rocket exploded Sunday on a congested street in the Karrada neighborhood of Baghdad. The Associated Press reported that the body of one victim lay in the street covered by a sheet.

The most intense fighting continued to be in Fallujah, a city 35 miles west of Baghdad that U.S. officials say is used by Zarqawi as a base for his operations.

Residents have become caught in the middle, with insurgents apparently clearing out neighborhoods to use for operations and U.S. forces responding with punishing airstrikes.

Mohammed Addai, 40, a welder, said, "The tragedy here is that these fighters are hiding among the people and they don't care about us, whether the houses are bombed are not."

Special correspondents Bassam Sebti and Omar Fekeiki contributed to this report.

Residents stand on the rubble of houses in Fallujah after U.S. airstrikes Saturday. Witnesses and hospital officials said 19 people were killed.