U.S. and Iraqi military officials say a suicide car bomber has killed at least 15 people at a market near Fallujah.
They say at least 13 others were wounded in the blast.
In other violence Tuesday, Iraqi police shot and killed a female suicide bomber as she approached a police recruitment center in Baghdad.
The U.S. military says an American soldier was killed Tuesday when his patrol was attacked with small-arms fire in southern Baghdad.
The military also says coalition troops detained 18 suspected terrorists in raids, including a suspected leader of al-Qaida in Iraq.
Meanwhile, U.S. and Iraqi troops are continuing the search for two missing soldiers, despite a video from an al-Qaida-linked group that claimed to have killed the men.
A military spokesman, Brigadier General Kevin Bergner said Monday the video did not contain any definitive evidence about the status of the soldiers.