The suspect was in a coma but has now regained consciousness and has talked to his lawyer.
Barack Obama, the US president, has ordered a review into how intelligence agencies handled information that they had gathered on Hasan before his alleged attack, the White House said on Thursday.
"I directed an immediate review be initiated to determine how any such intelligence was handled, shared, and acted upon within individual departments and agencies and what intelligence was shared with others," Obama said in a statement.
The order to conduct an "immediate inventory" of all intelligence in US government files was issued on November 6, a day after the shooting.
Investigators are trying to establish the motive behind the shootings, in which 12 soldiers and one civilian died.
But according to his family, Hasan, who was known to be against the US-led wars in Iraq and Afghanistan and was supposed to be deployed to Afghanistan this month, was trying to get out of the assignment.
US officials have said that intelligence agencies had previously investigated Hasan last December, reviewing what they believed to be email communications between him and a Muslim cleric in Yemen who was known for his anti-American teachings.
Federal officials ended the investigation after concluding that Hasan's communications were related to research he needed to work as a psychiatrist at the medical centre situated inside the US base.