The base's senior officer, Lt. Gen. Mark Milley, said there is a "strong possibility" that Spc. Ivan Lopez had a "verbal altercation" with another soldier or soldiers immediately before Wednesday's shooting, which unfolded on the same Army post that was the scene of an infamous 2009 mass shooting.
However, there's no indication that he targeted specific soldiers, Milley said.
Lopez never saw combat during a deployment to Iraq and had shown no apparent risk of violence before the shooting, officials said.
The 34-year-old truck driver from Puerto Rico seemed to have a clean record that showed no ties to extremist groups. But the Army secretary promised that investigators would keep all avenues open in their inquiry of the soldier whose rampage ended only after he fired a final bullet into his own head.
"We're not making any assumptions by that. We're going to keep an open mind and an open investigation. We will go where the facts lead us," Army Secretary John McHugh said, explaining that "possible extremist involvement is still being looked at very, very carefully."
Investigators were also looking into Lopez's psychological background. He had sought help for depression, anxiety and other problems, military officials said.
"We have very strong evidence that he had a medical history that indicates unstable psychiatric or psychological condition," Milley said. "We believe that to be a fundamental underlying cause."
Scott & White Memorial Hospital in nearby Temple, Texas, was still caring for several of the 16 people who were wounded. All of them were in either serious or good condition, and some could be discharged before the end of Thursday.
Hospital officials had no information about patients being treated elsewhere, including at a base hospital. But because Scott & White is the area's only trauma center, the patients with the most serious injuries were probably taken there.
Investigators searched the soldier's home Thursday and questioned his wife, Fort Hood spokesman Chris Haug said.
Lopez apparently walked into a building Wednesday and began firing a .45-caliber semi-automatic pistol. He then got into a vehicle and continued firing before driving to another building. He was eventually 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, Milley said.
Lopez grew up in Guayanilla, a town of fewer than 10,000 people on the southwestern coast of Puerto Rico, with a mother who was a nurse at a public clinic and a father who did maintenance for an electric utility company.
Glidden Lopez Torres, who said he was a friend speaking for the family, said Lopez's mother died of a heart attack in November.
The soldier was upset that he was granted only a 24-hour leave to attend her funeral, which was delayed for nearly a week so he could be there, the spokesman said. The leave was then extended to two days.
Lopez joined the island's National Guard in 1999 and served on a yearlong peacekeeping mission in Egypt's Sinai Peninsula in the mid-2000s. He enlisted with the Army in 2008 and saw no combat during a four-month deployment to Iraq as a truck driver in 2011, McHugh said.
A review of his service record showed no Purple Heart, indicating he was never wounded. He arrived at Fort Hood in February from Fort Bliss, Texas.
He saw a psychiatrist last month and showed no "sign of any likely violence either to himself or others," McHugh said.
Suzie Miller, a 71-year-old retired property manager who lived in the same Killeen apartment complex as Lopez, said few people knew him and his wife well because they had just moved in.
"I'd see him in his uniform heading out to the car every morning," Miller said. "He was friendly to me and a lot of us around here."
The shootings revived memories of the November 2009 shooting at Fort Hood, the deadliest attack on a domestic military installation in U.S. history. Thirteen people were killed and more than 30 were wounded.
Army psychiatrist Nidal Hasan was convicted last year in that assault, which he has said was to protect Islamic insurgents abroad from American aggression. After that shooting, the military tightened base security nationwide.
Associated Press writers Ramit Plushnick-Masti in Houston; Christopher Sherman in McAllen; Robert Burns, Eric Tucker and Alicia Caldwell in Washington; and Dánica Coto in Guayanilla, Puerto Rico.