At least 13 people, including Alexis, died in the attack. The 34-year-old civilian Navy contractor was identified by his fingerprints, NBC News reported.
The FBI posted his photo on the agency's website and asked the public's assistance with any information regarding Alexis, who was born in New York City's Queens borough. His last known residence before coming to Washington was Forth Worth, Texas.
Anyone with information about Alexis was asked to contact the FBI's Washington field office at 202-278-2000 or 1-800-CALL-FBI.
"No piece of information is too small," said Valerie Parlave, assistant director in charge of the office. "We are looking to learn everything we can about his recent movements, his contacts and associates."
NBC said the FBI believes Alexis used another man's identification card to access the Navy Yard. The man whose ID card was used was taken into custody and questioned by police, NBC said.
KXAS-TV, Fort Worth, said Alexis was living in New York when he enlisted in the Navy in May 2007. He graduated boot camp as an airman recruit and served in the reserves for four years. He became an aviation electrician's mate and served as a petty officer third class at the Naval Air Station Joint Reserve Base in Fort Worth until he was discharged on Jan. 31, 2011.
NBC News said police records show Alexis was arrested on a misdemeanor charge in Forth Worth in September 2010 for allegedly discharging a firearm within city limits. The police report says a shot was fired from Alexis' apartment through the ceiling into his upstairs neighbor's apartment. He said he was cleaning his gun when it slipped and he accidentally pulled the trigger. He admitted, however, to having a contentious relationship with the neighbor.
The Tarrant County District Attorney's office did not file charges in the case, KXAS reported Monday. "After reviewing the facts presented by the police department, it was determined that the elements constituting recklessness under Texas law were not present and a case was not filed," prosecutors said in a statement.
The Seattle Police Department said Alexis was arrested in 2004 for shooting out the tires of another man's vehicle in what Alexis later described as an anger-fueled "blackout."
The police report said Alexis told detectives he felt he was being mocked by construction workers and said they had "disrespected him."
"He claimed he had an anger-fueled 'blackout,' and could not remember firing his gun at the victims' vehicle until an hour after the incident," the police department said.
The police department said detectives later spoke with Alexis' father in New York, who said Alexis had anger management problems associated with post-traumatic stress disorder. His father said Alexis was an active participant in rescue attempts on Sept. 11, 2001.