Investigators believe Shane Tamura, of Las Vegas, was trying to get to the NFL offices after shooting several people on Monday in the building’s lobby but accidentally entered the wrong set of lifts, Mr Adams said in interviews on Tuesday.
Four people, including an off-duty New York City police officer, were killed.
Police said Mr Tamura had a history of mental illness, and a rambling note found on his body suggested he had a grievance against the NFL over an unsubstantiated claim that he suffered from chronic traumatic encephalopathy (CTE).
He had played American football in high school in California nearly two decades ago but never in the NFL.
“He seemed to have blamed the NFL,” the mayor said. “The NFL headquarters was located in the building, and he mistakenly went up the wrong elevator bank.”
The note claimed he had been suffering from CTE – the degenerative brain disease that has been linked to concussions and other repeated head trauma common in contact sports — and said his brain should be studied after he died, two people familiar with the matter told the Associated Press.
It also specifically referenced the National Football League, one of the people familiar with the matter said.
The note also referenced former NFL player Terry Long, who was diagnosed with CTE, and the manner in which Mr Long killed himself in 2005. The note accused the NFL of concealing the dangers to players’ brains for profit.
NFL commissioner Roger Goodell called the shooting “an unspeakable act of violence in our building”, saying he was deeply grateful to the law enforcement officers who responded and the officer who gave his life to protect others.
The shooting took place at a skyscraper that is home to the headquarters of both the NFL and Blackstone, one of the world’s largest investment firms, as well as other tenants.
The company confirmed one of its employees, Wesley LePatner, was among those killed.
“Words cannot express the devastation we feel,” the firm said in a statement. “Wesley was a beloved member of the Blackstone family and will be sorely missed. She was brilliant, passionate, warm, generous, and deeply respected within our firm and beyond.”
A Yale graduate, Ms LePatner was a real estate executive at Blackstone, according to the firm’s website, and spent more than a decade at Goldman Sachs before joining the firm in 2014.
Surveillance video showed the man exiting a double-parked BMW just before 6.30pm carrying an M4 rifle, then marching across a public plaza into the building.
Then, he started firing, police commissioner Jessica Tisch said, killing a police officer working a corporate security detail and then hitting a woman who tried to take cover as he sprayed the lobby with gunfire.
The man then made his way to the lift bank and shot a guard at a security desk and shot another man in the lobby, the commissioner said.
“Our officer, he was slain in the entryway to the right as soon as he entered the building, the suspect entered the building,” Mr Adams said in a TV interview. “He appeared to have first walked past the officer and then he turned to his right, and saw him and discharged several rounds.”
The man took the lift to the 33rd floor offices of the company that owned the building, Rudin Management, and shot and killed one person on that floor. The man then shot himself, the commissioner said. The building, 345 Park Avenue, also holds offices of the financial services firm KPMG.
The officer killed was Didarul Islam, 36, an immigrant from Bangladesh who had served as a police officer in New York City for more than three years, Ms Tisch said at a news conference.
“He was doing the job that we asked him to do. He put himself in harm’s way. He made the ultimate sacrifice,” ms Tisch said. “He died as he lived. A hero.”
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