An off-duty New York City police officer who had just finished his shift shot and killed a man during a traffic dispute early on Monday, the authorities said.

The officer, whom the police did not immediately identify by name, fired three rounds from his 9-millimeter service pistol after he and the other driver came to a stop at a red light on Atlantic Avenue in the Cypress Hills neighborhood of Brooklyn, the authorities said.

Delrawn Small — who was traveling with a woman and their children, two girls ages 5 months and 14 years — was killed, the police said. (The authorities said records showed his surname was Small, though they noted that his relatives said it was Dempsey.) No one else was injured.

The gunshots were fired at 12:06 a.m. and followed a dispute between the two men that had occurred along Atlantic Avenue. But the details of what set off the dispute — whether, for example, one driver had cut the other off — were not immediately clear.