Before buying the Remington 870 shotgun and the ammunition, he used a store rifle at a practice range, and he was at the store for at least a couple hours, Slocum said.
Video of Alexis at the store has been given to the FBI, according to Slocum.
4:04 p.m. ET -- Police in Newport, Rhode Island, say Alexis contacted them while he was staying there in August, complaining that he was hearing voices and was worried that three people were harassing him, according to CNN's Deborah Feyerick.
Newport police say they contacted the Newport naval base in August about their encounter with Alexis, who was working there as an information-technology contractor.
Alexis told Newport police that during a flight from Virginia to Rhode Island, he got into a "verbal altercation" with someone, Newport Police Lt. William Fitzgerald said.
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.