Officer Dalsh Veve, 35, remains in critical condition at Kings County Hospital, where he underwent surgery Sunday.
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He is "still very much fighting for his life," said NYPD Commissioner James O'Neill, who said he met with the officer's wife Monday morning.
The teen remains at Brookdale University Hospital, where he walked in with a gunshot wound to the face.
The officer was critically injured around midnight Sunday when the driver he was questioning in a possible shooting took off, authorities say.
The officers determined later that the likely cause of the 911 calls for shots fired was fireworks.
Veve was dragged for 2 1/2 blocks near Tilden Avenue and East 53rd Street in East Flatbush. The officer eventually became free and fell onto the street.
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The vehicle continued for a short distance before it crashed and was abandoned on East 53rd Street.
Surveillance cameras captured the incident as the driver took off.
Since Veve discharged his weapon twice while being dragged, the suspect was "most likely" shot by Veve, according to O'Neill.
Police say it remains unclear how Veve got dragged. "We believe he was holding onto the door. And at some point he was inside" the car," said NYPD Chief of Detectives Robert Boyce.
The teen has 11 previous arrests, most recently for grand larceny on May 16. He was charged with stealing a car in April, burglary in 2016, and three separate robberies in 2015.
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Police said the black Honda Civic that he was driving was stolen from a person delivering a pizza in Valley Stream on Long Island May 16.
Two women who were in the vehicle at the time of the dragging incident, 19-year-old Eboni Clinton and 18-year-old Jeronda Oliver, were charged with one count of hindering prosecution.
The officer is married and has a 2-year-old daughter. He is a nine-year veteran of the NYPD.
"He took his job very very seriously," said Mayor Bill de Blasio. "Rose up quickly within the precinct, doing some of the most important work that the precinct does. He is a strong man physically and mentally and we are all praying that strength will see him through in this very difficult moment."