The base's commander, Lt. Gen. Mark Milley, made the remarks about Spc. Ivan Lopez's health a day after officials said his mental condition appeared to be an underlying factor in the attack.
On Friday, Milley said that an "escalating argument" precipitated the assault.
Also Friday, Lopez's father said his son had struggled with the recent deaths of his mother and grandfather and the stress of being transferred to a new base.
Lopez's father, who shares the same name, said his son was receiving medical treatment but was a peaceful family man and a hard worker.
"This is very painful for me," the elder Lopez said in the statement from his native Puerto Rico, calling for prayers for the dead and the 16 people who were wounded in the shooting rampage. "My son could not have been in his right mind. He was not like that."
Wednesday's attack was the second at the base since 2009, when 13 people were killed by Army psychiatrist Nidal Hasan, who had said he was angry about being deployed to Afghanistan.
Lopez, an Army truck driver, did a short stint in Iraq in 2011 and told medical personnel he had suffered a traumatic brain injury. The 34-year-old was undergoing treatment for depression and anxiety while being evaluated for post-traumatic stress disorder, base officials said.
But officials said Lopez did not see any combat in Iraq, and had not previously demonstrated a risk of violence.
He seemed to have a clean record that showed no ties to potential terrorists, though military officials said the investigation was ongoing.
A family spokesman said Thursday that Lopez was upset he was granted only a 24-hour leave to attend his mother's funeral in November. That leave was then extended to two days.
Three people who were critically injured in the attack improved to fair condition Friday at Scott & White Memorial Hospital in Temple. A fourth victim was expected to be released later in the day. At the military's request, the hospital said, it would not make the wounded or their families available for media interviews.
Also Friday, Texas Gov. Rick Perry and Sen. Ted Cruz visited 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.
Investigators searched Lopez's home on Thursday and questioned his wife, who declined to comment in Spanish when reached by phone by The Associated Press.
Lopez walked into a base building around 4 p.m. Wednesday and began firing a .45-caliber semi-automatic pistol. He then got into a vehicle and continued shooting before entering another building on the Army post. He eventually was confronted by military police in a parking lot, Milley said.
As he came within 20 feet of a police officer, the gunman put his hands up but then reached under his jacket and pulled out his gun. The officer drew her own weapon, and the suspect put his gun to his head and pulled the trigger a final time, Milley said.
Coto reported from San Juan, Puerto Rico.