The New York attorney general has launched an investigation into a road-rage killing in which a New York police officer shot dead an unarmed driver in Brooklyn, said officials.

Delrawn Small, 37, reportedly became infuriated while driving in East New York in Brooklyn when he was cut off by a car driven by three-year NYPD officer Wayne Isaacs, 37, who was heading home on 5 July after his police shift.

When both cars came to stop at a red light, Small is alleged to have exited his vehicle and started punching the officer in the head through his open window, according to city authorities. Small was captured on surveillance video camera approaching Isaacs' car.

Isaacs pulled out his 9mm service pistol and shot Small point blank three times, reported the New York Daily News. Small was pronounced dead at the scene.

Small's girlfriend Zaquanna Albert and her baby son and two daughters witnessed the confrontation from Small's car. "My heart aches for this man and my son who will never remember his dad," she posted on her Facebook page. "Even if the man did attack you, roll up your window, drive off — hold yourself to a higher standard," said a relative of Small's Jermaine Gabriel. "Yeah, you can get upset. But to kill a man?"

Albert reportedly told police that Small was easy to anger and ignored her pleas not to confront Isaacs.

Eric Soufer, a spokesman for New York Attorney General Eric Scheniderman, said prosecutors had obtained a search warrant for the Isaacs' car and were "actively reviewing the case." The attorney general's office had also been in contact with police and Small's family, he said. City police are also investigating the shooting.

Small had an arrest history that included 19 offences. He spent three terms behind bars. He finished parole on his latest arrest for assault in 2013, according to records.

Isaacs was accused in a 2014 lawsuit of a false arrest in which the suspect was "punched, kicked and struck several times in the head and body."