Fitzgerald says Alexis told police "he was a naval contractor who travels often." He explained that during a flight from Virginia to Rhode Island, he got into a "verbal altercation" with an individual. Alexis told police he believed that the "individual had sent three people to follow him and to talk, keep him awake and send vibrations into his body," Fitzgerald said.
According to a police report, Alexis said he first heard the people talking to him through a wall at a Middletown hotel where he was staying. He packed up and went to an unidentified hotel on the naval base where he heard the same voices talking to him, so he moved to a third hotel.
According to Fitzgerald, Alexis heard the people "speaking to him through the floor and then ceiling." Alexis said the individuals were "using a microwave machine to send vibrations through the ceiling, penetrating his body so he could not speak."
Fitzgerald said Alexis would not elaborate or tell police what his alleged harassers were saying, but he told police "he never felt anything like this and felt these individuals would harm him."
Earlier Tuesday, a source with direct knowledge of the investigation told Feyerick that Alexis exhibited signs of mental problems in recent months and tried to get help at a Veterans Affairs facility in Rhode Island.
3:27 p.m. ET -- Alexis bought a shotgun from Sharpshooters Small Arms Range in the last few weeks, an attorney for the store said, according to CNN's Chris Lawrence.
The attorney, J. Michael Slocum, said Alexis had a valid driver's license, and the gun shop "did the full required background check, the same that's done when someone buys a weapon of any sort." Slocum indicated there was nothing in the background check to stop the sale to Alexis.
Slocum also said the FBI visited the store once since Monday's shooting, and that the store is cooperating with the investigation.
The FBI has said the Alexis used a shotgun in the shooting.
2:28 p.m. ET -- The news conference is over. Some more highlights from D.C. Police Chief Cathy Lanier: She said that within seven minutes of the first emergency call, police had at least two units inside the building where the shooting was happening.
The first unit arrived at the yard itself within two minutes of the call. It took police a while to determine which building was the shooting site, because callers were giving different building numbers, she said.
Security personnel from several agencies had "multiple engagements" with Alexis before the final shots were fired, she said.
2:23 p.m. ET -- More from the news conference: D.C. Police Chief Cathy Lanier elaborated on why she thinks the officer who was shot in both legs will make a full recovery, when there had been questions Monday of whether he would walk again.
"We have a very good prognosis from the doctors," Lanier said. She said that because of his personality, she believes that he will eventually be "outrunning all of us."
2:15 p.m. ET -- More from the news conference: The Washington police officer who was shot in both legs Monday is doing well, D.C. Police Chief Cathy Lanier said. He had surgery Monday.
"We expect he will make a full recovery," Lanier said.
Earlier, CNN's Chris Lawrence reported that physicians were expected to begin determining Tuesday whether the officer would be able to keep the limbs.
Also, Lanier said at the news conference that there's "no doubt in my mind" that the officers responding to the shooting "saved numerous lives."
2:11 p.m. ET -- More from the news conference: Alexis arrived in the Washington area on or about August 25, staying in hotels, said Valerie Parlave, assistant director in charge of the Washington FBI field office.
He most recently stayed at a Residence Inn in southwestern Washington, D.C., beginning around September 7, she said. Anyone who contacted him during that time should contact the FBI, she said.
2:08 p.m. ET -- FBI and other officials have begun a news conference in Washington, updating reporters on the investigation.
Alexis entered the yard's building 197 -- where the shooting took place -- with a shotgun, and investigators believe he obtained a handgun inside the building after he started shooting, Valerie Parlave, assistant director in charge of the Washington FBI field office, said moments ago at a news conference. This confirms what federal law enforcement sources said earlier.
2:01 p.m. ET -- U.S. Defense Secretary Chuck Hagel is ordering a worldwide review of physical security measures at all U.S. military installations in the wake of Monday's shooting, a senior Pentagon official said Tuesday, according to CNN's Barbara Starr.
Hagel will order the military to look at all existing security measures to see if they are sufficient and to determine what other measures may be needed, the official said.
At the same time, the Pentagon is still trying to determine what it needs to do to begin a parallel review of security clearances and access standards for contractors and other employees, according to a Defense Department official. Some elements of clearance procedures are handled by other parts of the government so coordination will be required, but the official said it's expected some review of that element will also take place.