Included in the claims are two cases accusing US soldiers of wrongful deaths of Iraqi civilians.
Colonel Guy Shields said 2,517 claims have been filed – 1,168 of which have already been processed. There have also been 328 additional claims that have been denied.
"So far we have received two wrongful death claims. They have yet to be adjudicated," he told reporters in Baghdad on Tuesday.
"We are still in the process of adjudicating 1,021 claims," the vast majority of which seek compensatory damages for property ruined during US military raids and other coalition activities, Shields said.
The total figure amounts to an average of 25 claims per day since US President George W Bush declared an end to major combat three months ago.
The US army has been criticised for heavy-handed tactics it has used in the hunt for ousted leader Saddam Hussein and former loyalists suspected of conducting attacks on coalition forces.
On Monday, the US military acknowledged its troops killed four Iraqi civilians when they opened fire on at least one car during a raid in an upmarket Baghdad district on 27 July.
"So far we have received two wrongful death claims. They have yet to be adjudicated."
-Colonel Guy Shields
Lieutenant General Ricardo Sanchez expressed regret over the casualties, but the case has raised added concern among Iraqis as civilian loss of life increases.
But Shields pointed to one case in which compensation was promptly provided for destruction of property.
Coalition forces conducted a pre-dawn raid in Baghdad, detaining two individuals. The pair were soon released and given taxi fares to get back home, he said.
"Yesterday morning coalition forces paid restitution for the damage done to the buildings" during the raid, he said.
The colonel did not say how much money was paid out, nor were statistics provided about other cases.