* Shooter served in Iraq, was being evaluated for PTSD
* Army base is site of 2009 rampage that left 13 dead
* President Obama says he is "heartbroken" (Adds details on background investigation, mental health of shooter, officials' comments)
By Lisa Maria Garza
FORT HOOD, Texas, April 3 (Reuters) - Investigators delved into the background Thursday of a U.S. soldier who had been treated for mental illness before he killed three people and himself a day earlier at an Army base in Fort Hood, Texas, where another deadly rampage took place in 2009, military officials said.
There was no motive given for the incident, although officials ruled out terrorism. The shooting also wounded 16 others, and the gunman, who had been treated for depression and anxiety, was yet to be officially identified.
The victims were all military personnel at the massive Army base, which houses many soldiers who have seen combat abroad.
The soldier had served four months in Iraq in 2011 and was undergoing evaluation for post-traumatic stress disorder, said Fort Hood commanding officer Lieutenant General Mark Milley.
Security officials said preliminary information identified the gunman as Ivan Lopez, but Milley declined to name the shooter, who is married, until his family was notified.
The suspect's wife was cooperating with law enforcement officers, a Federal Bureau of Investigation official said, according to CNN.
The shooter had "self-reported" a traumatic brain injury after returning from Iraq but was never wounded in action, Milley said. He arrived in Fort Hood in February from another military installation.
"We are digging deep into his background," Milley said, with the investigation looking at his mental health and criminal and combat history.
At about 4:00 p.m. local time (2100 GMT) on Wednesday, the soldier went to two buildings on the base and opened fire before he was confronted by military police, Milley said.
The gunman then shot himself in the head with a .45-caliber pistol, he said. U.S. Representative Michael McCaul of Texas told reporters the man was wearing an Army uniform.
Milley said law enforcement was looking into reports of an argument at the base ahead of the shooting.
"At this time there is no indication that this incident is related to terrorism," Milley told a news conference.
The rampage is the third shooting at a military base in the United States in about six months that, along with a series of shootings in schools and malls, has sparked a national debate over gun-control regulations.
The Scott & White Hospital in Temple, Texas, where some of the wounded were taken, said nine patients were in intensive care, of which three were in critical condition and six were stable.
Other victims were taken to Fort Hood's Carl R. Darnall Army Medical Center, near the site of the shooting.
U.S. President Barack Obama said he was "heartbroken" another shooting had occurred, and that the incident "reopens the pain of what happened at Fort Hood five years ago."
"We are going to get to the bottom of exactly what happened," Obama said.
The incident highlights the U.S. military's so-far frustrated efforts to secure its bases from potential shooters, who increasingly appear to target the facilities.
Milley said the shooter walked into one of the unit buildings, opened fire, then got into a vehicle and fired from there. He then went into another building and opened fire again, until he was engaged by Fort Hood law enforcement officers.
When confronted by a female military police officer, he shot himself with his semi-automatic weapon in the parking lot.
"He was approaching her at about 20 feet. He put his hands up, then reached under his jacket, pulled out the (.45) and she pulled out her weapon and then she engaged, and he then put the weapon to his head," Milley said.
One of the buildings housed medical brigade day-to-day operations and the other, nearby, served the administration of the transportation battalion.
As soon as the shooting broke out, the base went on lockdown. Police secured the base perimeter, emergency vehicles rushed to the scene, helicopters circled Fort Hood and officers went from building to building searching for the shooter.
Fort Hood, a base from which soldiers prepare to deploy to Iraq and Afghanistan, had overhauled its security to better deal with potential "insider threats" after a 2009 rampage by an Army psychiatrist who shot dead 13 people and wounded 32 others.
During that attack, Major Nidal Hasan shouted "Allahu Akbar," Arabic for "God is greatest," and later said he wanted to be a martyr. He was convicted and faces death by lethal injection.
In September, a gunman opened fire at the Washington Navy Yard, killing 12 and wounding four before being killed by police. Last month, a civilian shot dead a sailor aboard a ship at a U.S. Navy base in Norfolk, Virginia.
U.S. Defense Secretary Chuck Hagel ordered steps to improve Pentagon security after reviews found the Navy Yard shooting could have been averted if the gunman's mental health had been properly handled. (Additional reporting by Jana J. Pruet in Dallas, Jeff Mason in Chicago, David Alexander, Caren Bohan, Mark Hosenball in Washington, and Phil Stewart in Honolulu; Writing by Jon Herskovitz, Dina Kyriakidou and Eric M. Johnson; Editing by Louise Ireland and Bernadette Baum)