"As briefed last night, we believe at this time that the deceased shooter, Aaron Alexis, acted alone," FBI Assistant Director Valerie Parlave said. "As such with no other suspects at large the investigation has moved into a phase of evidence recovery and information gathering."
All 13 victims, including the shooter, have been identified.
Officials released the names of the 12 people killed by Alexis: Michael Arnold, 59; Martin Bodrog, 54; Arthur Daniels, 51; Sylvia Fraiser, 53; Kathy Gaarde, 62; John Roger Johnson, 73; Frank Kohler, 50; Mary Francis Knight, 51; Kenneth Bernard Proctor, 46; Vishnu Pandit, 61, Gerald L. Read, 58; and Richard Michael Ridgell, 52.
Alexis was killed in a gun battle with police that ended the attack.
Alexis, 34, entered Building 197 -- the Naval Sea Systems Command headquarters -- Monday morning "with a valid pass" armed with a shotgun and may have gained access to a handgun once inside the building after he began shooting, the spokeswoman told reporters at a briefing. She said she had no information on media reports that Alexis was armed with an AR-15 assault rifle during the attack.
"We also continue to conduct all other necessary investigation to learn about the activities and conduct of Mr. Alexis," she said.
A Defense Department official said Secretary Chuck Hagel would order a review of physical security and access to all military facilities nationwide, the department said in a tweet.
CNN said Alexis, a Navy reservist, had previously contacted two Veterans Administration hospitals because of what sources indicated were psychological issues.
NBC News reported Aug. 7 Alexis called police in Newport, R.I., to report he was hearing voices in the closet of his hotel room and claimed people were following him and that he had argued with them at the airport.
Alexis described them as two black men and a black woman, but he told police he was fine and did not need any help. A police check on him turned up no outstanding warrants, NBC said.
Hagel joined Joint Chiefs of Staff Chairman Gen. Martin Dempsey in placing a wreath next to the "Lone Sailor" statue at the memorial on Pennsylvania Avenue to honor the victims during a brief, sober ceremony as a bugler played "Taps."
The mourners were joined by Navy Secretary Ray Mabus and Washington Mayor Vincent Gray.
Early Tuesday, authorities cleared the final 2,000 people held on the base following the rampage, Navy officials said.
The FBI interviewed every person leaving the former shipyard and ordnance plant in southeast Washington, said Vice Adm. Bill French, the head of all Navy installations.
The shooting, which wounded at least five people, was the second-deadliest mass murder on a U.S. military base, after the November 2009 mass shooting at Fort Hood, Texas, that left 13 people dead. A metropolitan police officer wounded in the shootings was "doing well," said District of Columbia Police Chief Cathy Lanier
The Navy Yard shooting was also the deadliest mass murder in the Washington area since the Sept. 11, 2001, attack on the Pentagon that killed 184 people.
Authorities said they were still seeking a motive for the killings. They asked the public for help by posting pictures of Alexis on the FBI website.
The agency said it was treating the shooting as a criminal investigation, not one linked to terrorism.
French warned March 21 that one of the side-effects of the federal government's budget sequestration would be a reduction in Navy Yard security, Army Times reported at the time.
Alexis received a general discharge from the Navy Reserve in Fort Worth two years ago, a designation that usually signals a problem in his record.
"There is no question there was a pattern of misconduct," a defense official told several news organizations.
The official said Alexis was pushed out of the military after a 2010 arrest for firing a gun at his Fort Worth apartment. The incident sent a bullet into a neighbor's property a few days after an alleged confrontation with the neighbor over noise.
No one was injured and no charges were filed, said the Tarrant County Criminal District Attorney's Office in Fort Worth.
Alexis had told police "he was trying to clean his gun while cooking and that his hands were slippery," said the police report, cited by The Wall Street Journal.
Alexis was also arrested but not charged in a 2005 Seattle gun incident, officials said. NBC News said law enforcement officials had found no evidence supporting claims Alexis had participated in rescue operations after the Sept. 11, 2001, terror attacks.
Despite his record, he had a security clearance with a military contractor that gave him access to the Navy Yard, the officials said.
The Navy Yard was reopened Tuesday for essential personnel only, CBS News said.