Federal law enforcement authorities said Tuesday the gunman in the bloody mass murder at the Washington Navy Yard was a paranoid nutcase who had been hearing voices in his head.

Navy vet Aaron Alexis, 34, of Queens had been treated since August by the Veterans Administration for his mental problems, the officials told the Associated Press.

The Navy had not declared him mentally unfit, which would have rescinded a security clearance that Alexis had from his earlier time in the Naval Reserves.

Family members also told investigators that Alexis – a Thai-speaking Buddhist – who fatally gunned down 12 people and wounded 14 others – was being treated for his mental issues.

Alexis went on his murderous rampage at the Washington Navy Yard Monday morning, sparking widespread chaos before cops shot him dead, authorities said.

He started his killing spree at 8:20 a.m. — just as employees at the Navy Sea Systems Command building arrived for work — silently stalking the hallways on two floors and shooting sniper-style into the lobby to pick off his targets.

“No words. He raised the gun and started firing. He said nothing,’’ Sea Systems executive assistant Todd Brundidge told NBC.

A native of Kew Garden Hills who has family in Brooklyn, he had a government contractor access card issued to civilians, and used it to gain entry into the heavily guarded compound, officials said.

He also had an ID belonging to Rollie Chance, a retired Chief Petty Officer with the Navy who was initially identified as the shooter before Alexis was confirmed as the suspect.

Chance’s sister, Tanya Denise Chance of Brooklyn, said Tuesday morning she didn’t know if her brother knew the shooter.

“I haven’t spoken to my brother for a couple of weeks. I know about the shootings but I didn’t hear anything about my brother,” she said. “I wonder how he got my brother’s ID, do you think he stole it?”

Armed with a semiautomatic AR-15 rifle and a shotgun, Alexis took a guard’s handgun before he spent at least the next half-hour stalking his victims.

As the killer silently moved through the halls of Building 197, panicked workers were heard screaming to each other, “Where is he?! Where is he?!’’

Someone pulled a fire alarm to warn others, and after hearing it, Brundidge and his colleagues ran into the hallway — and came face-to-face with the killer.

“He was down the hall, and he stepped around the corner,’’ Brundidge said, adding the gunman was dressed all in blue.

“He aimed his gun at us, and he fired two or three shots. We ran down the stairs to get out of the building,’’ Brundidge told CNN. “After we left, there were still shots.”

A co-worker, Terrie Durham, said the group avoided slaughter by mere inches.

“He aimed high and missed . . . We’re lucky he was far enough away he was a bad shot,’’ she said.

There were conflicting accounts of casualties. The Navy said 14 people were hurt, but Washington Mayor Vincent Gray said eight were injured, including three who were shot.

Navy Capt. Mark Vandroff, 46, said he and eight other workers ran to a nearby third-floor conference room and barricaded themselves inside.

“We were all lying on the ground. But when we looked up, about eight feet off the floor, there were bullet holes in the walls,’’ he said.

At one point, the gunman shot sniper-style from a fourth-floor walkway overlooking the lobby, targeting people outside the cafeteria on the first floor.

“It was three gunshots straight in a row — pop, pop, pop,’’ said Patricia Ward. “Three seconds later, it was pop, pop, pop, pop, so it was like about a total of seven gunshots.”

Navy Cmdr. Tim Jirus said he fled into an alley in the back of the building and wound up standing next to another man as two shots were fired at 8:45 a.m.

Jirus told The Post that he turned around to see where the gunfire was coming from and, by the time he spun back around, the man beside him had been fatally shot in the head.

“It’s crazy. You come to work on a Monday, and the next thing you know, there are people inside your building shooting the people you work with,’’ Jirus said.

On Monday night, officials released the names of seven of the slain victims, all civilians: Michael Arnold, 59; Sylvia Frasier, 53; Kathy Gaarde, 62; John Roger Johnson, 73; Frank Kohler, 50; Kenneth Bernard Proctor, 46; and Vishnu Pandit, 61.

A neighbor of Kathy Gaarde in Prince William County, Va., told The Washington Post Monday night that she was the “kindest lady in the world.”

“She just helped make it a good home for her family and worked hard,” Patrick Bolton said.

The vice president of LMI, a consulting firm where Michael Arnold worked, told the paper he was a “great American.”

“People liked working with Mike,” said Jeff Bennett. “He was just a solid, solid citizen.”

Some 2,000 people were still in the naval complex more than 12 hours after the shootings. One worker was found after hiding in a locker for 11 hours.

The wounded included DC Metro Police Officer Scott Williams, who took two bullets to the leg, The Washington Post said.

Washington Hospital Center said it treated the cop and two women and all were expected to survive.

Authorities did not give details on how Alexis died after being hunted down by heavily armed SWAT-team members, some wearing night-vision goggles.

The FBI Monday night said he was the lone gunman, despite reports during the day that a second shooter was being sought.

He had purchased the shotgun he used in Lorton, Va., and was believed to have stayed at the Residence Inn in Washington, DC, for a few weeks before the attack.

He was identified by his fingerprints, after being found with the ID of former Defense Department worker Rollie Chance.

Alexis had been working for The Experts, a Hewlett-Packard subcontractor, and had security clearance and a government contractor access card that allowed him access to the Navy Yard.

He worked on a contract to refresh internal Navy and Marine computer systems around the world. He had finished work for the company in Japan and was being reassigned to a new contract at the Navy Yard, The Experts CEO Thomas Hoshko said.

Two friends told CNN that Alexis was recently involved in a money dispute with the firm.

But Mayor Gray told reporters, “We don’t know what the motive [for the attack] is.”