He has called for prayers for the victims of his son’s attack at Fort Hood in Texas on Wednesday.
A military investigator said on Friday there was evidence the soldier had been in an argument before opening fire, killing three and wounding 16 others.
But officials do not see his mental condition as the reason for the attack.
The shootings took place at two buildings at Fort Hood at about 16:00 local time, when Specialist Ivan Lopez, who had the same name as his father, is alleged to have walked into one of the buildings and opened fire with a .45-calibre semi-automatic pistol.
He then got into a vehicle and continued firing before entering another building and opening fire again. He was eventually stopped by military police, shooting himself in the head when confronted by a female officer in the car park, officials say.
The dead men were formally named on Friday as Sgt First Class Daniel Ferguson, 39. Staff Sgt Carlos Lazaney-Rodriguez, who was 38, and 37-year-old Army Sgt Timothy Owens.
“My son could not have been in his right mind. He was not like that,” Spc Ivan Lopez’s father wrote in a statement from the family’s home in Puerto Rico on Friday.
The motive for the shooting is unclear and Fort Hood’s base commander Lt. Gen. Mark Milley said on Friday that investigators did not consider his mental state the “immediate precipitating factor”.
In contrast, Lt. Gen. Milley had spoken the previous day of the post-traumatic stress disorder Spc Lopez had suffered after serving in Iraq, suggesting there was strong evidence he had “an unstable psychiatric or psychological condition”.
But in his latest remarks he said the cause “was more likely an escalating argument in his unit area”.
His words were echoed by Chris Grey, spokesman for the U.S. Army Criminal Investigation Command, who said there was “credible information he was involved in a verbal altercation with soldiers from his unit just prior to him allegedly opening fire”.
But he added there was still “no concrete motive” for the attack and it might never be known why the shooting had taken place.
Fort Hood was also the scene of a gun rampage in 2009 that left 13 soldiers dead and 32 wounded.
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