Testifying before a military trial over alleged abuse of Iraqis by US forces, Major Robert Gwinner said Lieutenant-Colonel Nate Sassaman had ordered soldiers to lie about the bridge incident to the Army's Criminal Investigation Command, or CID.
One of the two Iraqis is thought to have drowned in the Tigris.
"They did not want CID to know that the Iraqis had gone into the water," Gwinner said.
The major was testifying in the court martial of army Sergeant First Class Tracy Perkins, who faces more than 25 years in military prison on charges of involuntary manslaughter, aggravated assault and obstruction of justice.
Perkins is accused of killing Zaidun Hassun, 19, by having subordinates force him off a ledge above the Tigris at Samarra in Iraq.
Marwan Fadil, who was also forced off the bridge along with his cousin Hassun, testified on Wednesday that US soldiers tossed the two at gunpoint into the water and laughed as his relative drowned.
The two Iraqis had been detained shortly before an 11pm curfew on 3 January 2004.
Punishing curfew violators by pushing them into water was probably within troops' discretion, Gwinner said. "It was within the scope of non-lethal force, but not one that we recommend, or we will use again."