Alexis, a former Navy reservist who struggled with mental-health problems and other issues, used his secret-level clearance Monday to gain access to the secure Navy Yard compound, where he fatally shot a dozen people before being killed by police.
Comey said the civilian contractor was not targeting individuals during Monday's rampage.
The gunman appeared intent on killing as many people as possible during the shooting spree, which went on for more than 30 minutes, stopping only when he was cornered by police and ran out of ammunition. "He was isolated and pinned down by the first responders," the FBI director said at a news briefing.
There was no discernible pattern to the shooting.
He was "calmly moving without any particular direction or purpose. It was not as if he was looking for any particular person or group," Comey said.
Alexis had been working in the building as a civilian contractor and was familiar with the layout of the building.
It was still unclear Thursday how Alexis got the weapon into the building, the Los Angeles Times reported. Comey said the gun may have been in the bag Alexis carried in that morning or it might have been planted inside the bathroom.
Comey said there is no sign Alexis had help from anyone.
Thursday was a regular work day at the Navy Yard, except at Building 197, which remained closed. WRC-TV, Washington, reported.
Only essential employees were asked to work on Tuesday and Wednesday.
Defense Secretary Chuck Hagel said the military didn't pick up on "red flags" that could have stopped the shooting spree.
"Obviously, when you go back in hindsight and look at this, there were some red flags," Hagel told reporters Wednesday at the Pentagon.
"Should we have picked them up? Why didn't we? How could we have? All those questions need to be answered," he said.
Among the missed cues were a U.S. Navy failure to follow up on a Rhode Island police report six weeks ago indicating Alexis, a Navy contractor, reported hearing voices and being followed by people using a microwave machine to disrupt his sleep.
Alexis also visited Veterans Affairs hospital emergency rooms twice in the last month saying he couldn't sleep. Doctors gave him medicine.
During the Providence visit Aug. 23 and the Washington visit Aug. 28, Alexis told doctors he didn't have anxiety, depression or violent thoughts, The Wall Street Journal reported.
If he had spoken about hurting himself or others, that would have required doctors to alert authorities of potential danger, the Journal said.
The VA also said Alexis was paid $395 a month as a disability benefit, in part because he had tinnitus, which is the perception of sound, such as ringing of the ears, when no external sound is present.
Hagel said he ordered a broad review of security and background procedures to figure out what shortfalls exist in the process.
"Obviously, something went wrong," he said. "We will review everything, and from that review, we would hope that we will find some answers to how we do it better."
Besides the security clearance review, Hagel said he would appoint an "independent panel" to look into security at military installations and screenings of people who have access to sensitive information.
"Where there are gaps, we will close them," he said. "Where there are inadequacies, we will address them. And where there are failures, we will correct them. We owe the victims, their families and all our people nothing less."