Nicholas Ivie, 30, was shot and killed after he and two other agents responded to a tripped sensor about five miles north of the Mexico/Arizona border on Tuesday. Another agent was wounded in the attack, and the third agent was not injured.
The probe is looking into whether the two agents exchanged gunfire Tuesday in the mistaken belief that each was being fired on by a hostile gunman.
An investigation into the shooting is being handled by the FBI and the Cochise County Sheriff's Office. At FBI headquarters, spokesman Chris Allen declined to comment.
A Mexican law enforcement official said on Thursday that two people were in custody in connection with the shooting, but it was not yet clear if there was strong evidence linking the men to the attack.
The Associated Press contributed to this report.