Within hours of the the attack, investigators started looking into whether the man's combat experience had caused lingering psychological trauma.
Fort Hood's senior officer, Lt Gen Mark Milley, said the gunman had sought help for depression, anxiety and other problems.
Among the possibilities investigators planned to explore was whether a fight or argument on the base triggered the attack.
The official said authorities would begin by speaking with the man's wife, and expected to search his home and any computers he owned.
The shooter was identified as Ivan Lopez by Texas Representative Michael McCaul, chairman of the House Homeland Security Committee. But the congressman offered no other details, and the military declined to identify the gunman until his family members had been notified.