One NYPD vehicle can be seen parked against a barrier in the middle of the street when a second NYPD vehicle drives into a large group.
A law enforcement official said the officer hit the gas after realizing a flaming bag was on top of the vehicle.
Mayor Bill de Blasio later said police were surrounded and had to get away, but that he also found the video troubling.
"I didn't like what I saw one it. I did not want to ever see something like that. I don't want to ever see it again. And clearly we need to do a full investigation and look at the actions of those officers and see what was done and why it was done and what could be done differently," he said. "But I also want to emphasize that situation was created by a group of protesters blocking and surrounding a police vehicle, a tactic that we had seen before in the last few days, a tactic that can be very, very dangerous to everyone involved and we have seen direct attacks on police officers, including in their vehicles, and we need a full and impartial investigation but we also need to be clear about the context."
"You have to be in those officers' shoes," NYPD Police Commissioner Shea said of the footage.
Shea said some peaceful demonstrations were "hijacked" by a small number of people with violent intent.
The independent review ordered by de Blasio will be conducted by New York city Corporation Counsel James Johnson, who is the city's chief lawyer, and Margaret Garnett, commissioner of the Department of Investigation, which typically investigates suspected wrongdoing and fraud by city employees.
With more protests scheduled Sunday, Shea said his officers will work with demonstrators.
"We're going to make sure that everyone has the right to peacefully protest and assemble," Shea said said at a briefing with the mayor. "But we are not going to tolerate destruction of property, having our officers put into harm's way or any civilians put into harm's way."
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