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 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."