A gunman who opened fire in the centre of New York City and killed four people allegedly left a note that appeared to blame the National Football League (NFL) for a brain injury.

The shooter, 27-year-old Shane Tamura from Las Vegas, took his own life after shooting inside a glitzy Manhattan skyscraper that is home to the Irish consulate and firms including Blackstone and the NFL on Monday, July 28.

The city's Mayor, Eric Adams, said the assailant was carrying a note saying that he believed he had CTE, a form of brain injury triggered by blows to the head.

He also said Tamura played football when he was a teenager but didn't play for the NFL, according to CBS News.

"[Tamura] did have a note on him, Adams told CBS.

"The note alluded to that he felt he had CTE, a known brain injury for those who participate in contact sports."

Legions of emergency vehicles rushed to the skyscraper at 345 Park Avenue following the shooting.

A police officer, named locally as Didarul Islam, was among the victims.

Islam was working private security at the time and was said to have been shot in the back.

In tribute to the officer, New York City Police Department (NYPD) said: "He was protecting New Yorkers from danger when his life was tragically cut short today.

"We join in prayer during this time of incomprehensible pain. We will forever honour his legacy."

Tamura died of a self-inflicted gunshot wound, senior New York City officials said.

Preliminary checks did not show a "significant criminal background", officials told CNN.