The demonstrators had gathered to protest a confrontation with U.S. troops that began Monday night. The International Committee of the Red Cross said 15 Iraqis were killed in that clash. 

In Wednesday's violence, the captain in charge of U.S. forces told CNN's Karl Penhaul that Iraqi protesters fired at a U.S. convoy as it passed a demonstration and that U.S. forces fired warning shots -- then may have fired on the demonstrators. 

Iraqi protesters said the first shot came from U.S. forces. 

One U.S. soldier said: "All I know is a couple hundred people gathered out in the streets; they threw rocks, so we shot back, and they all ran down that way." 

Protesters carried the bodies of the two people killed Wednesday in coffins through the streets of Fallujah. 

The demonstrators on Monday night had marched to the school at the request of a local Muslim cleric to demand that U.S. troops withdraw from the building so classes could resume. (Full story) 

U.S. military officials said shots had been fired by protesters as well as by gunmen using automatic weapons from nearby rooftops. Iraqi witnesses said the protesters threw rocks. 

American soldiers displayed one AK-47 and two Kalashnikov rifles seized afterward, but it was not clear whether the weapons had been recently fired. 

The situation in Fallujah is under investigation, Pentagon officials said. U.S. military officials said they are meeting with local officials to determine how to best handle such events. 

Violence elsewhere in Iraq
A U.S. soldier on civil affairs duty was shot Tuesday near downtown Baghdad's Palestine Hotel, U.S. Central Command said. 

The soldier was taken to a field hospital, but the wounds were not considered life-threatening, according to Central Command. A gunman could not be found. 

Central Command said four soldiers on a public health-related mission in downtown Baghdad were ambushed and wounded Sunday. All were in stable condition Tuesday. 

Maj. Gen. Buford Blount, commander of the U.S. Army's 3rd Infantry Division that controls Baghdad, said there had been a number of incidents in which snipers had fired on U.S. troops in Baghdad. Most of the attackers were either killed or arrested, Blount said. 

Blount said the main priority of his troops was maintaining security in the Iraqi capital. 

His soldiers guard 150 facilities in the city -- including power stations, water treatment plants, schools and banks -- and have found more than 500 ammunition caches in schools and residential areas, he said. Ten-ton trucks move out 500 tons of seized munitions each day, he said.