Investigators believe Shane Tamura, of Las Vegas, was trying to get up to the NFL offices after shooting several people in the lobby on Monday but entered the wrong elevator bank, Mayor Eric Adams said in interviews.

Four people were killed, including an off-duty New York City police officer, Didarul Islam.

Tamura, who played high school football in California nearly two decades ago but never in the NFL, had a history of mental illness, police said.

A three-page note found in his wallet suggested he had a grievance against the NFL over a claim that he suffered from chronic traumatic encephalopathy.

The degenerative brain disease has been linked to concussions and other repeated head trauma common in contact sports such as football, but it can only be diagnosed after someone has died.

In the note, Tamura repeatedly said he was sorry and asked that his brain be studied for CTE, according to the police department.

The note also referenced former NFL player Terry Long, who was diagnosed with CTE, and the manner in which Long killed himself in 2005. The note accused the NFL of concealing the dangers to players’ brains for profit.

The NFL long denied the link between football and CTE, but it acknowledged the connection in 2016 testimony before Congress and has paid more than $US1.4 billion ($2.15 billion) to retired players to settle concussion-related claims.

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.

Goodell said in a memo to staff that a league employee was seriously injured in the attack and was hospitalised in stable condition.

The shooting happened along Park Avenue, one the nation’s most recognised streets, and just blocks from Grand Central Terminal and Rockefeller Centre.

It’s also less than a 15-minute walk from where UnitedHealthcare CEO Brian Thompson was shot and killed last December by a man who prosecutors say was angry over corporate greed.

President Donald Trump said on Tuesday that he knows that area of Manhattan well.

“I trust our Law Enforcement Agencies to get to the bottom of why this crazed lunatic committed such a senseless act of violence. My heart is with the families of the four people who were killed, including the NYPD Officer, who made the ultimate sacrifice,” Trump posted on social media.

The building houses the NFL and other well-known businesses

Investigators found that Tamura drove across the country over the past few days and made his way into New York City just before the shooting, Police Commissioner Jessica Tisch said.

Surveillance video showed the gunman exiting a double-parked BMW early on Monday evening with a rifle, then marching across a plaza and into the skyscraper, which is also home to investment firm Blackstone and other companies. It was closed Tuesday except to investigators.

He then sprayed the lobby with gunfire, killing Islam, who was off-police duty and working a corporate security detail, and hitting a woman who tried to take cover, Tisch said.

He next made his way to the elevator bank, shooting a guard at a security desk and another man in the lobby, the commissioner said.

“He appeared to have first walked past the officer and then he turned to his right, and saw him and discharged several rounds,” Adams said in a TV interview.

Tamura took an elevator to the 33rd-floor offices of the company that owns the building, Rudin Management, and shot and killed one person on that floor. He then shot and killed himself, the commissioner said.

Blackstone confirmed that one of its employees, real estate executive Wesley LePatner, was among those killed. Security officer Aland Etienne also died, according to a local labor union.

The officer who was killed was from Bangladesh

Islam, 36, had served as a police officer in New York City for three-and-a-half years and was an immigrant from Bangladesh, Tisch said at a news conference.

His body was draped in the New York Police Department flag as it was moved from the hospital to an ambulance, with fellow officers standing at attention.

“He was doing the job that we asked him to do. He put himself in harm’s way. He made the ultimate sacrifice,” Tisch said. “He died as he lived: a hero.”