There were no indications that Alexis had any ideological differences with the Navy or any disagreements with anyone at the Navy Yard, the U.S. law enforcement official said.
Alexis' family reeled at the news that he was believed to be the man behind the killings.
"What I do know is he wasn't that type of person," Anthony Little, who identified himself as Alexis' brother-in-law, told reporters outside his Brooklyn, New York, home. "I didn't really hear anything that would make me feel, as a newcomer to the family, that somebody should be watching him."
He said the family's initial reaction was "very distraught, very stressed out, tears."
"You know, they didn't see it coming," said Little, who is married to Alexis' sister Naomi. "Their hearts are going out more to the victims and the people that got hurt because, you know, there's more lives lost and we don't need that right now. We really don't."
Alexis, who was from New York City, served as a full-time Navy reservist between 2007 and 2011, according to military records.
In the Navy, he achieved the rank of aviation electrician's mate 3rd class, working on aircraft electrical systems, the records show.
Alexis was honorably discharged after a "pattern of misconduct," a U.S. defense official with knowledge of the investigation told CNN on condition of anonymity. The official did not detail the misconduct.
Most recently, Alexis worked as an information technology contractor with the Navy, Secretary of the Navy Ray Mabus told CNN's Wolf Blitzer.
Alexis appeared to have had sporadic run-ins with the law, dating back to at least 2004 when he was arrested in Seattle, accused of shooting out the tires of a man's truck in an anger-fueled "blackout," according to a Seattle Police Department report.
He told investigators he believed the man, a construction worker, was mocking him, but had no memory of shooting out the tires, the report said.
Investigators later spoke with Alexis' father, who told police that his son had anger management problems associated with post-traumatic stress disorder, which he suffered after working "as an active participant in rescue attempts" during the September 11, 2001, terrorist attacks in New York, the report said.
Alexis was arrested in August 2008 on a charge of disorderly conduct in DeKalb County, Georgia, county police said Tuesday.
And in 2010, Alexis was arrested by Fort Worth, Texas, police but never charged over an allegation that he fired a gun through the ceiling of his apartment. According to records, he told police he accidentally fired it while cleaning it.
His last known address was outside of Fort Worth, where he was roommates for three years with Nutpisit Suthamtewakul, who described Alexis as his best friend.
Alexis befriended Suthamtewakul four years ago after he emigrated from Thailand.