The incident - the latest in a series of clashes and deadly shootings involving U.S. troops in Fallujah - came as President Bush prepared to address to the American public from a homeward-bound aircraft carrier, declaring that major combat in Iraq is finished.
Capt. Frank Rosenblatt says none of the injuries to soldiers of the 3rd Armored Cavalry Regiment in Fallujah is believed to be life-threatening.
The troops inside the walled compound - a former police station - opened fire on men fleeing the area, but no one was captured or believed hit, said Rosenblatt, whose 82nd Airborne Division is handing over control of Fallujah to the Armored Cavalry.
The attackers' identities were unknown, Brig. Gen. Dan Hahn, chief of staff for the Army's V Corps, said in Baghdad.
The attack, at 1 a.m. Thursday, came after soldiers in the compound and in a passing Army convoy opened fire Wednesday on anti-American demonstrators massed outside. Local hospital officials said two Iraqis were killed and 18 wounded.
American officers said that barrage was provoked when someone fired on the convoy from the crowd.
Wednesday's march was to protest earlier bloodshed Monday night, when 16 demonstrators and bystanders were killed and more than 50 wounded, according to hospital counts. In that clash, an 82nd Airborne company, whose members said they were being shot at, fired on a protest outside a school occupied by U.S. soldiers.
Some Fallujah residents said they had heard relatives of victims vow to avenge Wednesday's shootings - and many in the city have declared they want the American troops to leave.
Resistance to American troops is especially sharp in Fallujah, a city of 200,000 people 30 miles west of Baghdad, because it benefited more than most from Saddam Hussein's regime.
The regime built chemical and other factories that generated jobs for Fallujah's workers and wealth for its businessmen. Many of Fallujah's young men joined elite regime forces such as the Republican Guard and Special Republican Guard.
In other developments:
White House spokesman Ari Fleischer says Mr. Bush will stop short of declaring victory or saying the war is over. Such declarations could trigger international provisions requiring the speedy release of prisoners of war and limit efforts to go after defeated Iraqi leaders.
In Fallujah, U.S. military officials met Wednesday with local religious and clan leaders on the security situation.
"We asked the commanding officers for an investigation and for compensation for the families of the dead and injured," said Taha Bedaiwi al-Alwani, the new, U.S.-recognized mayor of Fallujah.
Al-Alwani and other Iraqis also asked that U.S. troops be redeployed outside the city center. A U.S. paratrooper company has already left one school where it were staying, which was the focus of Monday's protest.
Residents told reporters they are troubled by soldiers who gaze on Fallujah women, and some believe the Americans' goggles or binoculars could "see" through curtains or clothing.
Elsewhere in Iraq, troops of the 4th Infantry Division raided a house late Wednesday in Tikrit, Saddam's hometown, and arrested a local official of Saddam's Baath Party who was accused of trying to run a "shadow regime" opposing coalition forces.
U.S. troops refused to release the official's name.
Five Bradley Fighting Vehicles surrounded the two-story villa in a neighborhood formerly reserved for Baath Party members. One of the Bradleys slammed through a 10-foot wall surrounding the compound. About 40 infantrymen swarmed through the hole, fanning across the lawn and breaking down the wooden front door.
Inside, the soldiers found three men - the suspect and his two sons - five women and four children. The three men were led from the house blindfolded, their hands bound behind their backs.
In Baghdad, the U.S.-led team charged with rebuilding Iraq's civil society has been screening government employees trying to return to work.
The 150 people who showed up at the Planning Ministry on Wednesday faced tough scrutiny from the U.S. Office of Reconstruction and Humanitarian Assistance, which is struggling to weed out Baath Party officials and potential provocateurs from the ranks of a reconfigured civil service.
Charles Heatly, a spokesman for the reconstruction office, said U.S. and British officials had met with bureaucrats at most of the 23 ministries that operated under Saddam's regime. Many were eager to return to work.
As plans for the new government proceeded, three top leaders of the opposition to Saddam met in Baghdad to discuss how they would work together.
Ahmad Chalabi of the Iraqi National Congress, Massoud Barzani of the Kurdistan Democratic Party and Jalal Talabani of the Patriotic Union of Kurdistan began a series of meetings Wednesday night, according to the INC's London office. It offered no details, citing security, but said more meetings were planned.
Many Iraqis are suspicious of Chalabi because he lived in exile for years and did not suffer alongside them under Saddam.
Former U.S. President Clinton, attending a political conference in Mexico City, said the United States needs to involve more countries, and the United Nations, in rebuilding Iraq.
"We cannot let this be a precedent for weakening the U.N.," said Mr. Clinton. "We have to have honest inspections for chemical and biological weapons, and we need to have a sensible attempt to involve the world in building a democratic Iraq."