WASHINGTON (Reuters) - The death toll left by an army psychiatrist who went on a shooting rampage at a U.S. military base in Texas rose to 13 on Friday, U.S. media reported.

Suspected gunman Major Nidal Malik Hasan opened fire with two handguns at the Fort Hood Army post on Thursday, in one of the worst killing sprees ever reported on a U.S. military base, army officials said.

A woman died overnight from gunshot wounds, raising the toll to 13 dead and 30 wounded, CNN reported.

Hasan, who was shot several times, was unconscious but in stable condition and on a ventilator, CNN said.

Lieutenant-General Robert Cone, Fort Hood's commanding officer, told CNN that the FBI and military forensic experts were investigating the shooting.

The Army said the lone gunman opened fire at the Soldiers Readiness Processing Centre, a group of buildings where soldiers were getting medical check-ups before leaving for overseas deployments.

Cone said the gunman had two weapons, one of them a semi-automatic. He said there was no indication that they were military weapons and the evidence does not suggest the shooting was a terrorist attack.

Hasan, 39, is a military-trained psychiatrist who had treated soldiers wounded in war or were preparing at the post for foreign deployment.

The U.S.-born Muslim is the son of Palestinian immigrants and was raised in Virginia. He served as a psychiatrist at the Walter Reed Army Medical Centre in Washington, D.C., which treats many badly wounded troops.

A cousin of the suspected shooter, Nader Hasan, told Fox News that he had been ordered to serve a term in Iraq and had been resisting deployment there.

Hasan said his cousin had been transferred to Fort Hood in April and was very reluctant to go to Iraq. "We've known over the last five years that was probably his worst nightmare," he said.

U.S. President Barack Obama called the event a "horrific outburst of violence" and promised "answers to every single question about this horrible incident."

Fort Hood is home to about 50,000 troops and stretches across 339 square miles (878 square km) in central Texas, halfway between Austin and Waco.

(Reporting by Anthony Boadle, editing by Vicki Allen)