FORT HOOD, Texas — An Army psychiatrist set to be shipped overseas opened fire at the Fort Hood Army base Thursday, authorities said, a rampage that killed 12 people and left 31 wounded in the worst mass shooting ever at a military base in the United States.

The gunman, first said to have been killed, was wounded but alive and in stable condition under military guard, said Lt. Gen. Robert W. Cone, commanding officer at Fort Hood. “I would say his death is not imminent,” Cone said.

Col. Ben Danner said the suspect was shot at least four times and was in critical condition.

The suspect was identified as Maj. Nidal Malik Hasan, 39, an eight-year military veteran from Virginia.

President Obama called the shooting at the Soldier Readiness Center, where soldiers who are about to be deployed or who have just returned undergo medical screening, “a horrific outburst of violence.”

“It’s difficult enough when we lose these brave Americans in battles overseas,” the commander in chief said. “It is horrifying that they should come under fire at an Army base on American soil.”

There was no official word on a motive. The shooter used two handguns, one of them semiautomatic, Danner said, and neither was military-issued.

Hasan had transferred to Fort Hood in July from Walter Reed Medical Center in Washington, where he received a poor performance evaluation, according to an official who spoke on condition of anonymity because he was not authorized to discuss the case publicly.

Sen. Kay Bailey Hutchison, R-Texas, said generals at Fort Hood told her that Hasan was about to deploy overseas. Retired Army Col. Terry Lee, who said he had worked with Hasan, told Fox News that he was being sent to Afghanistan.

Lee said Hasan had hoped Obama would pull troops out of Afghanistan and Iraq and got into frequent arguments with others in the military who supported the wars.

Officials were investigating whether Hasan was his birth name or if he may have changed his name, possibly as part of a conversion to Islam. However, they were not certain of his religion.

The Washington Post reported that he attended the Muslim Community Center in Silver Spring, Md., and was devout, according to Faizul Khan, former imam at the center. He attended prayers at least once a day, seven days a week, often in his Army fatigues, Khan told the newspaper.

The New York Times reported that Hasan was the child of Palestinian immigrants from a small town near Jerusalem.

Video from the scene showed police patrolling the area with handguns and rifles, ducking behind buildings for cover. Sirens could be heard wailing while a woman’s voice on a public-address system urged people to take cover.

“I was confused and just shocked,” said Spc. Jerry Richard, 27, who works at the center but was not on duty during the shooting. “Overseas you are ready for it, but here you can’t even defend yourself.”

Soldiers at Fort Hood don’t carry weapons unless they are doing training exercises.

The Rev. Greg Schannep was about to head into a graduation ceremony when a man in uniform approached him, warning him that someone had opened fire. Schannep heard three volleys of gunfire and saw people running.

“There was a burst of shots and more bursts of shots and people running everywhere,” said Schannep, who works for Rep. John R. Carter, R-Texas.

The uniformed man who had warned him ran to the theater. Schannep said he could see that the man’s back was bloodied from a wound. The man survived, was treated and will be fine, Schannep said.

Cone said initially that three people were taken into custody and that all have been interviewed. Authorities believe, however, that there was a single shooter.

The Soldier Readiness Center holds hundreds of people and is one of the most populated parts of the base, said Steve Moore, a spokesman for III Corps at Fort Hood.

The wounded were taken to hospitals in central Texas, Cone said. Their identities, and the identities of the dead, were not immediately released.

Amber Bahr, 19, was shot in the stomach but was listed in stable condition, said her mother, Lisa Pfund of Random Lake, Wis.

“We know nothing, just that she was shot in the belly,” Pfund told the Associated Press. She could not provide more details and only spoke with emergency personnel.

Hasan, whose family said he was born in suburban Washington, is single with no children. He graduated from Virginia Tech University, where he was a member of the ROTC and earned a bachelor’s degree in biochemistry in 1997. He received his medical degree from the military’s Uniformed Services University of the Health Sciences in Bethesda, Md., in 2001 and was at Walter Reed for six years for his internship, residency and a fellowship.

“We are shocked and saddened by the terrible events at Fort Hood today,” his cousin, Nadar Hasan, said in a statement issued on behalf of their family. “We send the families of the victims our most heartfelt sympathies.”

No other shooting at a military base in the United States has been anywhere near as deadly as Thursday’s. In 1993, a gunman at Fort Knox, Ky., shot five civilian co-workers, killing three, and then fatally shot himself.

Across the country, some military bases stepped up security precautions, but no others were locked down.

Covering 339 square miles, Fort Hood is the largest active-duty post for armored units in the United States. Home to about 52,000 troops as of earlier this year, it is located halfway between Austin and Waco.

Hasan had come to the attention of authorities six months ago because of Internet postings that discussed suicide bombings and other threats, law enforcement officials said. The officials say they are still trying to confirm that he was the author. They say an official investigation was not opened.

One of the Web postings that authorities reviewed is a blog that equates suicide bombers with a soldier throwing himself on a grenade to save the lives of his comrades.

“To say that this soldier committed suicide is inappropriate. Its more appropriate to say he is a brave hero that sacrificed his life for a more noble cause,” said the Internet posting. “Scholars have paralled (sic) this to suicide bombers whose intention, by sacrificing their lives, is to help save Muslims by killing enemy soldiers.”

Families, so used to being separated during long deployments, were separated again Thursday in a situation that to many seemed surreal.

“My friend’s husband called her from Iraq and said, ‘Isn’t it sad that I am safer over here in Iraq than you are at home?’ ” said Jessica Sullens, 28, who had spent hours in a nearby Walmart parking lot, where she had dashed on a midday errand.

Her own husband, Cpl. Thomas Sullens and their 1-and 2-year-old daughters were in lockdown on the base, he with his motor pool while the children were with a neighbor. “This is unreal to me,” Sullens said.

The Los Angeles Times contributed to this report.