The suspected gunman has been identified as Maj. Nidal Malik Hasan. Hasan would have been deployed to Iraq later this month, an Army official said.
It would have been his first deployment, two sources told ABC News.
Hasan is believed to be of Palestinian origin: His grandfather moved to the United States in the 1940s. One of Hasan's two brothers recently moved to Ramallah and works in the West Bank, the sources said. Hasan's family is said to own a number of apartments in Ramallah.
The person also said that all three brothers -- a lawyer, a professor and a psychiatrist -- are well educated. They lost both parents to cancer. Hasan's mother came from al Bireh, a Palestinian town close to Ramallah. She was traumatized by her experience in the 1967 Arab-Israeli war, when she was 15, according to the source.
Hasan was initially reported to have been killed in the Fort Hood attack but Lt. Gen. Robert W. Cone told a late-night news conference that the suspect was wounded and in custody. Cone declined to comment on Hasan's medical condition was but said he was expected to live.
Hasan has not spoken to authorities, Cone said.
Two other soldiers were taken into custody but were later released.
Hasan's cousin, Nader Hasan, issued a statement late Thursday. "We are shocked and saddened by the terrible events at Fort Hood today. We send the families of the victims our most heartfelt sympathies," the statement read.
"Nidal was an American citizen. He was born in Arlington, Va., and raised here in America. ... Our family loves America. We are proud of our country, and saddened by today's tragedy."
Hasan allegedly opened fire and killed 13 people on the post before he was shot several times. Among the wounded was a female police officer who exchanged gunfire with Hasan.
Cone called the attack "a terrible tragedy, stunning." He said the community was "absolutely devastated."
President Obama Pays Tribute to Fort Hood Victims
President Obama called the Fort Hood shootings a "horrific outburst of violence."
"It is difficult enough to lose soldiers overseas, but it is horrifying that they should lose their lives at an Army base in the U.S.," he said.
"My prayers are with the wounded and the families of the fallen," said the president.
The Senate and the House of Representatives held a moment of silence this evening for the victims of the Fort Hood massacre, and Texas Gov. Rick Perry ordered flags be flown at half mast until Sunday.
Cone said the motive for the attack, which took place just after 1:30 p.m. CT, is unclear. While he said he could not rule out the incident as an act of terrorism, evidence does not support that theory.
Hasan's cousin Nader Hasan said that she believed it was his upcoming deployment combined with the wartime horror stories he heard from his patients that set him off.
Hasan had reportedly recently hired an attorney to help him get out of the military.
According to the suspect's cousin, Hasan was also harassed after 9/11 because of his ethnicity, and was called a "camel jockey."
According to sources, Hasan, who is either 39 or 40, attended the Uniformed Services University of the Health Sciences in Bethesda, MD. He graduated in 2003 with a degree in Osteopathy and later finished his residency as a psychiatrist.
In 2009, Hasan completed a fellowship in Disaster and Preventive Psychiatry at the Center for Traumatic Stress.
He was promoted to major status in May, according to the Army Times.
According to the Associated Press, Retired Army Col. Terry Lee told Fox News that Hasan had expressed hope that President Obama would pull troops out of Afghanistan and Iraq and often argued with others who supported the wars.
Fort Hood Went on Lockdown After 12 Shot Dead
Fort Hood, located just 60 miles north from Austin, is the largest U.S. military installation in the world, and has suffered the greatest number of casualities of all American bases in the war on Iraq.
The base is a 340 sq. mile facility located in Killeen, Texas and is home to the 1st Cavalry Division, which was one of the first groups of soldiers deployed to Iraq.
Cone said that a gunman entered a facility known as the Soldier Readiness Facility, where soldiers who are preparing to deploy go for last minute medical check ups and dental treatment. Sources told ABC News that the soldiers gathered there were getting ready to deploy to Iraq.
Thursday is a day that brings many different military units to the facility to make up miss appointments, said Cone, which explains why the victims were part of different branches.
"This could have been much worse, as horrible as this was, it could have been much worse," said Cone.
Cone praised the soldiers' quick response and knowledge of first aid techniques in saving so many lives.
The gunman used two handguns, Cone said. He wasn't sure if the shooter reloaded the weapons during the attack.
Cone said he did not believe the guns used were military weapons.
"As a matter of practice, we don't carry weapons here, this is our home," said Cone.
Schools on the base were also placed on lockdown. A message on Fort Hood's public affairs office Web site read, "Organizations/units are instructed to execute a 100 percent accountability of all personnel. This is not a Drill. It is an Emergency Situation."
According to a source on the base, it is rare for firearms to be on the base because they are locked up.
Homeland Security said it is still gathering information and that the "Army is taking the lead" as of now. FBI agents from Waco and Austin, Texas, are being deployed to the scene.
An army spokesman said that unit commanders have been instructed to account for all of their personnel.
"The immediate concern is to make sure that all of our soldiers and family members are safe and that's what commanders have been instructed to do," said Jay Adams of First Army, Division West, located at Fort Hood.
Cone emphasized the post's plans to amp up security in the coming days.
The CounterTerrorist Unit said they have "no word" yet on whether this incident was terrorism-related.
At least six victims are being treated at the Metroplex Hospital five miles away. Area hospitals are all requesting blood donations to treat victims.
Nasser Atta contributed to the reporting of this story from Ramallah.