New South Wales police will assign an assistant commissioner to review an alleged road rage incident involving the state’s police minister, David Elliott, amid calls from the opposition for him to be sacked.

However, Guardian Australia understands the minister will not be stood aside, and the premier’s office considers it a matter for the police.

The Labor leader, Jodi McKay, said Elliott could also potentially be charged for impersonating a police officer when he told a 17-year-old P-plater that he “worked for the cops”.

Elliot has admitted making the claim but denied grabbing the teenager’s arm during the heated argument on a Sydney road, or chasing him through the Castle Hill back streets, as the boy’s father has claimed to the Australian.

“The NSW police commissioner has allocated northwest metropolitan region commander, assistant commissioner Mark Jones, to undertake an independent review of the matter,” a spokeswoman for NSW police said.

“All witnesses will be spoken to in order to ascertain if they’re in a position to provide any further information.”

McKay and the Labor opposition spokeswoman on police, Lynda Voltz, called on the premier, Gladys Berejiklian, to immediately sack Elliott.

“David Elliott simply cannot continue to be the police minister,” said McKay.

“The police minister is one of the most senior ministries in the NSW cabinet. What does it take for Gladys Berejiklian to stand down one of her ministers? What sort of standards is she applying to her police minister if she won’t sack him for this?”

Elliot said the teenage driver clipped his car and drove off on Windsor Road, Baulkham Hills, on 17 October.

He has admitted he “blew up” when the youth refused to exchange contact details and swore at his wife.

“He claimed he didn’t have to so I said I work for the cops,” Elliott said. “He didn’t believe me so I gave him my business card. He said: ‘Show me your badge.’ I said: ‘I pay for the badges, I don’t get one.’ ”

The boy’s father said that when his son phoned him during the verbal altercation, he could hear a man “yelling and screaming” in the background.

The Greens MP David Shoebridge said it should be interstate officers investigating because of a “significant conflict of interest” for the NSW force.

“Given the role of the police minister, it is clearly inappropriate for the NSW police force and its officers to investigate this matter so I am asking that you give urgent consideration to an interstate investigation into this incident,” he wrote to NSW police commissioner, Mick Fuller, in a letter seen by Guardian Australia.

“That the police minister appears to impersonating a NSW police officer risks the reputation both of the minister and of the NSW police force and on its own warrants an independent and thorough investigation.”

With the Australian Associated Press.