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The marked police car pursued the Peugeot 308 after it triggered a "positive hit" on an automatic number plate recognition system, Scotland Yard said.
The force added that the police car had its 'blues and twos' in operation at the time of the incident.
The father of a 13-year-old girl, who died in a crash involving a vehicle which was being pursued by police, remains in hospital for treatment to injuries, Scotland Yard said.
The girl's mother and brother, who were also travelling in the car, have been discharged from hospital.
A post-mortem examination on the teenager has been scheduled for tomorrow morning.
Speaking in the House of Commons, Home Secretary Theresa May said: "Could I also extend my sympathies to the family of the 13-year-old girl who died following a traffic accident involving a police patrol car on Sunday night.
"This matter is being investigated by the Independent Police Complaints Commission."
Traffic officers are investigating a crash involving a vehicle which was being pursued by police in New Cross, south London.
A 13-year-old girl died at the scene, her brother and parents are currently in hospital recovering from their injuries.
ITV Daybreak correspondent Jonathan Swain reports:
Commander Tony Eastaugh said:
Traffic police and officers from the Directorate of Professional Standards are now investigating, the force said.
The Independent Police Complaints Commission has also been informed and an investigator was at the scene assessing the circumstances of the collision.
The girl's parents and brother were taken to hospital and their injuries were not thought to be serious.
The male driver of the Peugeot was arrested and taken into custody. A female passenger was taken to hospital suffering from minor injuries.
The incident happened just before 6.30pm and police, ambulance and fire crews attended.
The Metropolitan Police said the pursuing police car had its blue lights and sirens on when the collision happened.
A 13-year-old girl has died in a crash involving a vehicle which was being pursued by police.
The teenager was travelling with her mother, father and brother in Ilderton Road, New Cross, south London yesterday when their Volkswagen Polo and a Peugeot 308 that was being chased by a marked police car collided.
The girl, who was in the rear of the car, died at the scene from her injuries, Scotland Yard said.