The station cited an unnamed law enforcement source as saying the team was less than 30 seconds from the base gate when the first call went out alerting police of the shooting.
The team was preparing to enter the facility in a bid to stop the gunman when the commander called them back to the Capitol, the station reported without attribution.
While Alexis' employer, an information technology contractor called The Experts, said it had no reports of trouble with him from Navy bases where he had worked over the summer, a picture was building of an increasingly troubled mind.
On August 7, Alexis told police in Newport, Rhode Island, that he believed he was being followed by three people who had been dispatched by someone with whom he'd quarreled, a police report said.
He said they had been sent to "follow him and keep him awake by talking to him and sending vibrations into his body," according to the report.
Alexis said he hadn't seen any of these people, but insisted they'd followed him between three hotels in the area -- the last being a Marriott, where police investigating a harassment complaint stopped to talk with him.
There, Alexis told authorities the unseen individuals continued speaking to him through walls and the floor. He said they used "some sort of microwave machine" to send vibrations into his body to keep him awake.
He added, according to the police report, that "he does not have a history of mental illness in his family and that he never had any sort of mental episode." Nonetheless, a police sergeant alerted authorities at Naval Station Newport to Alexis "hearing voices." Reached Tuesday, officials at the base referred CNN to the FBI, which declined to comment.
Benita Bell met Alexis last week at the Residence Inn where he was staying before the shootings.
On the Tuesday before the shootings, he seemed "engaging, present, connected," Bell told CNN. On Wednesday, he seemed markedly different -- stressed and hurried, she said.
"He said he was extremely tired, exhausted," Bell said.
Alexis' autopsy is expected to be completed by the end of the day Wednesday, according to a spokeswoman for the Office of the Chief Medical Examiner in Washington.
The Navy moved to discharge Alexis in 2010 due to what two Navy officials described as a "pattern of misconduct." Those incidents involved insubordination, disorderly conduct, unauthorized absences from work and at least one instance of drunkenness, a U.S. defense official told CNN.
Because of a lack of evidence, authorities were unable to get a general discharge that might have had an impact on his ability to get civilian work, the official said. Instead, he was given an honorable discharge and later hired as a civilian military contractor after passing security reviews.
There also were run-ins with police, beyond the Newport incident. Seattle police arrested Alexis in 2004 on accusations that he shot out the tires of another man's vehicle in what he later told detectives was an anger-fueled "blackout." He was arrested in 2008 in DeKalb County, Georgia, on a disorderly conduct charge.
Friends said Alexis didn't seem capable of such violence.
"Aaron was a very polite, very friendly man," said Kristi Suthamtewakul, a friend and former housemate.
But he was frustrated about pay and benefits issues after a one-month contracting stint in Japan last year, Suthamtewakul said.