"The aircraft had been flying in support of Operation Iraqi Freedom when contact was lost at approximately 10.10pm (1910 GMT) on 2 May," the statement on Wednesday said.
There was no initial indication of hostile fire in the area at the time contact was lost. The incident is still under investigation.
The name of the pilot is being withheld pending notification of the next of kin.
In Washington, a defence official said on Tuesday they suspected the two fighters collided in mid-air at 30,000 feet, but no final conclusion had been reached.
One official, who asked not to be identified, said an emergency beacon from one of the planes was located on the ground about 25km southwest of Karbala.
The body of the first pilot was found earlier in the week.