"The warplane was downed over arable lands. Witnesses confirmed that the plane was fired on by gunmen's rockets when it was flying on low altitude."
William Caldwell, a US military spokesman, said he would be surprised if the jet was shot down as the F-16's fly very fast and have not encountered any weapons capable of taking them down in Iraq.
A spokesman said that the aircraft was lost while it was flying in support of ground operations taking place in Fallujah.
US troops are reported to have surrounded the crash-site.
"We got credible news saying at 2pm on Monday a US F-16 warplane was downed in al-Garma neighbourhood near the western Iraqi city of Falluja"
Muthana Shakir, an Iraqi journalist in Baghdad
Send us your views
Elsewere in Iraq, sectarian violence continued on Monday after the government lifted a three-day curfew imposed on Baghdad at the weekend.
An interior ministry source said that five people were killed and at least eight wounded during a US army raid in Husainiya, a mainly Shia area on the northern outskirts of Baghdad.
Nassar al-Rubaie, a Shia politician from the Sadr movement, said that 15 civilians were killed and 20 wounded.
The US military said it was checking the reports and made no further comment.
Several people were also reported killed in the cities of Tel Afer and Ramadi.
Iraqi police also found five bodies dumped in Baghdad on Monday.
The US army also reported that three soldiers were killed on Sunday.