The commissioner said the upper floors that are home to residences do not have fire sprinklers.
The fire engulfed a large apartment on the 50th floor.
"Todd Brassner, 67, who was in the apartment, was taken to a hospital and died a short time later, the New York Police Department said".
It said the four firefighters had "non-life threatening" injuries and the blaze had been brought under control. An investigation is ongoing.
Plus, Brassner had reportedly still been alive when Trump issued his tweet.
The first family has an apartment on the top floors of the 58-story building, but President Trump has spent little time there since taking office in January 2017.
"It's a well-built building", Nigro said at a press conference.
Early talks for the proposed bill suggested that all residential buildings be required to install sprinklers, which irked developers, including Trump.
As New York City firefighters pushed through courageously, trying to save anyone caught in the disaster, President Donald Trump could only think of one thing while sitting comfortably in the White House: his brand. Under the 1999 legislation, buildings constructed before then were only required to have sprinklers if they underwent gut renovations.
The president tweeted that the fire was out, and had been "very confined" as the tower is a "well built building".
Multiple street closures slowed foot and vehicle traffic surrounding the tower, from East 55th Street to East 57th Street from Fifth Avenue to Madison Avenue, according to officials.
Nigro said units went up with the Secret Service to check Trump's residence.
Firefighters were sweeping adjacent apartments and stairwells to determine the source of the blaze in one of the skyscraper's residential apartments, according to fire officials. "If you look at the fire deaths in NY, nearly all of them are in one- or two-family houses".
Despite not receiving a notification from the skyscraper's management team to evacuate, the terrified 76-year-old managed to make it out alive.
A firefighter works in front of Trump Tower after a fire in New York, April 7, 2018.