Elsman was the sole victim in the crash, which occurred after 26-year-old Richard Rojas drove his auto down the sidewalk for three blocks into the heart of New York City's theater district before crashing into a security barrier.
Rojas was also charged with drunken driving in 2008 and 2015, according to New York City police.
"Based on the information we have at this moment, there is no indication that this was an act of terrorism", de Blasio said at a press conference at W. 42nd St. and Broadway.
He said he and a group of about five people chased the driver after he jumped out of the vehicle.
The incident took place close to noon on a bright, sunny day.
The driver of the vehicle, identified by police as Richard Rojas, 26, of the Bronx, was screaming and flailing as he got out of the auto after hitting multiple people, Bradix said. A woman's body lay covered with a bloodstained blanket.
Police officers secure the area near a vehicle after it plunged into pedestrians in Times Square in NY on May 18, 2017.
The crash killed an 18-year-old woman, and the injured included her 13-year-old sister, police said. Hundreds of thousands of people, many of them tourists from around the world, pass daily through the commercial area, the heart of the Broadway theater district.
The bustling streets are heavily patrolled by police, some on horseback.
Richard Rojas, 26, has lived with his mother in an apartment on Walton Avenue since the Navy imposed its most punitive sanction possible short of a court martial - a less-than-honorable discharge - in May 2014, a Pentagon source said.More news: Turkey's Erdogan and Trump: Kindred spirits, divergent agendas
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Police say an 18-year-old woman killed by a vehicle that plowed through pedestrians in Times Square was a tourist from Portage, Michigan.
His job classification was that of electrician's mate fireman apprentice, the records show.
Rojas has had multiple arrests, including two for driving while intoxicated, according to police. It was not immediately clear whether Rojas had a defense lawyer.
Navy records show that in 2013 he spent two months at a naval brig in Charleston, South Carolina, but didn't indicate the reason.
Mr Rojas reportedly told police: "You were supposed to shoot me, I wanted to kill them". Law enforcement sources told ABC News initial tests have come back negative for alcohol but positive for drugs.
The crash occurred outside the headquarters of the Reuters news agency, 3 Times Square. He said he looked out and saw what appeared to be a body in the street.
One of the injured, Cheryl Howard, had blood dripping down her right arm and a bruise above her left eye. She and her daughter were shopping when the auto sped toward them.
"I'm so freaked out!" Howard's daughter said. "They mowed everyone down".
A few hours after the Times Square incident, about 20 police officers and detectives occupied the sidewalk outside the six-story red brick building where Rojas lives.