Hasan, born in the US to Muslim Palestinian parents, was unconscious but in stable condition on Saturday.
He was transferred on Friday afternoon by helicopter to the Brooke Army Medical Centre in San Antonio, Texas, Rossi said.
He had been on a ventilator in a civilian hospital.
Flags at half mast
Barack Obama, the US president, met FBI officials, including Robert Mueller, the agency's director, on Friday to discuss the incident.
"We don't know all the answers yet and I would caution against jumping to conclusions until we have all the facts," Obama said.
He ordered flags at all federal buildings to be flown at half mast in tribute to those killed in the attack.
April 3, 2009: Jiverly Wong, a Vietnamese immigrant, opens fire at an immigrant community centre in Binghamton, New York, killing 11 immigrants and two workers. Wong killed himself at the scene
March 10, 2009: Michael McLendon, 28, killed 10 people, including his
Mother and four other family members in Alabama before himself committing suicide.
February 14, 2008: Former student Steven Kazmierczak, 27, kills five students and wound 18 more in shooting at Northern Illinois University in DeKalb. He then killed himself.
December 5, 2007: Robert Hawkins, 19, opens fire in a shopping mall in Omaha, Nebraska killing eight people before taking his own life.
April 16, 2007: Cho Seung-Hui, 23, kills 32 students and staff at Virginia Tech before killing himself in the deadliest mass shooting in modern US history.
Hasan, 39, had spent years counselling severely wounded soldiers at the Walter Reed Army Medical Centre in Washington, many of whom had lost limbs fighting in Iraq and Afghanistan.
He was transferred to Fort Hood in April and was to have been deployed to Afghanistan, where the US military is engaged in an increasingly bloody war against Taliban and al-Qaeda fighters.
Al Jazeera's Josh Rushing, reporting from Fort Hood, said: "[Hasan] joined the army after high school and went to the Virginia Tech university to get a psychiatry degree through a military programme.
"Every day, he heard how horrible those stories were and he really started to question the wars, according to what his cousin and sources who knew him said.
"Hasan became more devout in his religion and started arguing with soldiers about whether the wars were right or not, to the point where he received disciplinary action and negative work reviews.
"It raises a major question - how can a person responsible for the mental health of soldiers returning [from war] be allowed to continue in this profession when he has these kinds of questions himself?"
The Army Criminal Investigation Command and the FBI were investigating the shootings and no charges had been brought against Hasan, John McHugh, the US army secretary, said.
Hasan's cousin, Nader Hasan, said in interviews that he had been agitated about being deployed to be sent overseas.
"We've known over the last five years that was probably his worst nightmare," he said.
He told the New York Times newspaper that Hasan had retained a lawyer and sought to get out of the army before the end of his contract.
|The suspect has been named as Nidal Malik Hasan, an army psychiatrist [Reuters]
American Muslim groups expressed regret and stressed that the incident appeared to have been carried out by a single disturbed individual.
"Thousands of Arab Americans and American Muslims serve honorably every day in all four branches of the US military and in the National Guard," the Arab American Institute said on Friday.
Rossi said Thursday's shooting lasted about 10 minutes. He said a female civilian police officer was the first to wound Hasan, who was wearing military garb.
Further bloodshed was narrowly prevented when Hasan was apparently blocked from reaching a graduation ceremony attended by some 600 people, just metres away from the scene, Robert Cone, the Fort Hood base commander, said on Friday.
Multiple shooting incidents are not uncommon in the US, where there are relatively lax gun controls.
Fort Hood personnel have accounted for more suicides than any other army post since the US invasion of Iraq in 2003, with 75 tallied through July of this year.
The base, about 100km from the state capital, Austin, is home to about 50,000 troops.