April 2, 2014  -- The soldier who gunned down three colleagues today at Fort Hood before killing himself was a combat veteran who suffered from "mental issues" and was being evaluated for possible post-traumatic stress disorder, a Fort Hood commander said today.

Lt. Gen. Mark Milley declined to identify the shooter during a news briefing, but law enforcement and military sources told ABC News the assailant was Spc. Ivan Lopez. Milley said the shooter was assigned to the 13th Sustainment Command, which is based at Fort Hood in Killeen, Texas, and had served four months in Iraq in 2011.

A motive had not been identified, Milley said. He added that there was "no indication" the incident was related to terrorism, although investigators were not ruling anything out.

"Obviously, we are digging deep into his background," Milley said. "He was undergoing behavioral health, psychiatric treatment for depression and anxiety and a variety of other psychological and psychiatric issues. ... He was not diagnosed, as of today, with PTSD, he was undergoing a diagnosis process to determine if he had PTSD. That is a lengthy process."

READ: Fort Hood Alleged Gunman Identified as Spc. Ivan Lopez

In addition to the four deaths, 16 people were injured in the shooting, all members of the military, Milley said. At least three were in critical condition, according to one of the hospitals treating the survivors.

The exact sequence of events was not totally clear, Milley said, but it is believed that, starting around 4 p.m. local time, the gunman "walked into one of the unit buildings, opened fire, got into a vehicle, fired from [the] vehicle, got out of the vehicle, walked into another building, opened fire again and was engaged by local law enforcement here at Fort Hood."

At one point, Milley said, the gunman put his hands in the air, but then reached for his gun. When he did, an unidentified military policewoman engaged him. The gunman then shot and killed himself.

"It was clearly heroic, what she did at that moment in time," Milley said.

PHOTOS: Shooting at Fort Hood

The firearm used by the assailant was a semi-automatic, .45 caliber Smith & Wesson handgun, Milley said, adding that it was not registered on the base as base rules require.

The ATF was conducting an urgent trace of the gun, which is standard protocol in these types of incidents, law enforcement sources told ABC News.

Authorities initially were concerned another shooter might be at large and a "shelter in place" order remained in effect after the shooting. An all-clear siren sounded several hours after the shooting, reopening Fort Hood.

Today's violence brought back sharp memories from November 2009, when Army psychiatrist Maj. Nidal Hasan opened fire inside Fort Hood, killing 13 people. He was convicted and sentenced to death in August.

"Obviously, this reopens the pain of what happened at Fort Hood five years ago," Obama said during an impromptu appearance before reporters inside the Chicago Cut Steakhouse.

"We know these families. We know their incredible service to our country and the sacrifices that they make," he said. "Obviously, our thoughts and prayers are with the entire community, and we are going to do everything we can to make sure the community of Fort Hood has what it needs to deal with a tough situation, but also any potential aftermath."

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