Sgt. Jonathan Westbrook was shot four times, his father Theodis Westbrook told ABC News. He was struck twice in the arm and twice in the chest, but he survived and was released from the hospital on Friday.
Theodis Westbrook said his son told him Spc. Ivan Lopez became agitated after an employee asked him to come back the next day for a leave of absence form.
Lt. Gen. Mark Milley confirmed that an "escalating argument" precipitated the assault on Wednesday. He would not reveal the cause of the argument.
Jonathan Westbrook's sister told ABC affiliate WAPT that Lopez walked off exasperated when a supervisor told him to come back the next day, and then within minutes, he came back and started shooting, hitting the supervisor first.
Milley said investigators believe Lopez made no effort to target specific soldiers, even though at least one of the soldiers shot was involved in the argument.
Authorities identified the dead as 39-year-old Daniel Ferguson, of Mulberry, Fla.; 38-year-old Carlos Lazaney-Rodriguez, of Puerto Rico; and 37-year-old Timothy Owens, of Effingham, Ill. Ten of the 16 wounded soldiers have been released from hospitals, Milley said.
The gunman's father revealed that Lopez had struggled with the recent deaths of his mother and grandfather and the stress of being transferred to a new base.
Texas Gov. Rick Perry and Sen. Ted Cruz visited some of the wounded at a military hospital. Cruz said he was inspired by a soldier who had suffered a bullet wound to his abdomen, but still shielded other soldiers and called 911.
The Associated Press contributed to this report.