After speaking to the 82nd Airborne Division about Friday's crash, U.S. Army Brig. Gen. Mark Kimmitt said "they are fairly convinced that it was enemy fire" that downed the helicopter.
A policeman who saw the crash told Reuters that a missile hit the helicopter.
"We were in a joint patrol with U.S. troops to remove landmines and I saw a helicopter hovering in the sky which was hit by a missile," policeman Mohammad Abdul Aziz said. "It was split into two and went down in flames."
Friday's attack marks the fifth time a U.S. helicopter was shot down by guerrillas in Iraq in recent months. In November, insurgents brought down three Black Hawk utility helicopters and a Chinook transporter, killing a total of 39 U.S. soldiers.
After Friday's attack, U.S. soldiers swept through Fallujah, blocking off streets and searching homes and shops. Fallujah lies in the heart of the Sunni Triangle, which has been the site of near-constant attacks on U.S. forces.
Elsewhere in Iraq, an oil tanker in a U.S. convoy was set ablaze in an apparent attack by anti-American insurgents.
The tanker was traveling near a U.S. military base on the road to the western town of Ramadi when witnesses said a rocket or roadside bomb hit the convoy, according to the Associated Press.
Also on Friday, one soldier died and six were injured when a truck traveling toward Baghdad International Airport flipped on its side, the military said. The cause was under investigation.
Meanwhile in the northern, oil-rich city of Kirkuk, tensions between Kurds, Arabs and Turkmen led to more violence with conflicting reports of the exact number of casualties.
Kirkuk police commander Shirko Shakir told Reuters a protest late Thursday led to an exchange of gunfire with police, who detained a wounded Arab gunman. Another man, whose ethnicity Shakir declined to specify, was found killed in the area where the recent protests and clashes occurred, he said.
"From the amount of shooting we assume that there are more wounded and killed whose bodies they took away, and we are watching hospitals and private doctors for them," he told Reuters, blaming the violence on insurgents loyal to Saddam.
Jalal Jawher, the local head of the Kurdish faction the Patriotic Union of Kurdistan party, told the AP that there was a shootout Thursday night between Arabs and police, who killed two attackers and wounded several others.
Tensions in Kirkuk have been particularly high since an attack Wednesday on Arab and Turkmen protesters who were demanding that the city's 1 million residents remain under the administration of a central Iraqi government.
Some Kurds have been calling for the city to join autonomous Kurdistan, a Switzerland-sized area of northern Iraq where Kurds have had self-rule ruled since the end of the 1991 Gulf War under U.S.-led aerial protection.