Authorities say 44-year-old Elwaleed Mohamed pulled over at the intersection of East 65th Street and Madison Avenue to settle the dispute just after 12:25 a.m.
But instead of getting out himself, the driver of the Altima ran Mohamed down.
The male driver and female passenger of the Altima then allegedly ditched the car at the scene and fled on foot.
Mohamed, a loving husband and the father of two young boys, was pinned under his cab. Police had to use a hydraulic lift to remove him.
"He was completely under the car," witness Tony Benevento said. "He didn't move at all."
The taxi driver was pronounced dead at New York Presbyterian Hospital.
Authorities say the two occupants of the Altima ran north on Madison Avenue and then west on East 66th Street.
"I turned around and a guy and girl are running up the block," Benevento said.
As family and friends consoled Mohamed's wife inside her Brooklyn home, police tracked the car's owner to a high-rise apartment building in Harlem. There, Marvin Loyola said his cousin was the last person to drive the vehicle.
Loyola told Eyewitness News that he hasn't seen his cousin and knows nothing of the incident.
Meanwhile, the NYSFTD is offering a $3,000 reward for information leading to an arrest.
"Taxi drivers are the first faces millions of tourists see when visiting New York," said Fernando Mateo, spokesperson for the NYSFTD. "As representatives or ambassadors of the city, they need to be protected and cared for. They are hard working; they work under pressure, on holidays, and serve this city unconditionally on a regular basis. As ambassadors, they do not deserve to die the way this driver did this morning, in the line of duty."