Claiming that his driver Ashok Singh was at the wheels, Salman said in an affidavit filed on March 17 that the prosecution had failed to produce a single witness or a photograph showing that he was driving it.
The affidavit became public knowledge only on Wednesday.
The statement followed a notice issued by the apex court issued on February 19 on a Maharashtra government's petition challenging the Bombay High Court verdict acquitting the film star in the case.
The high court had on December 10, 2015 acquitted Salman, saying that the prosecution had failed to prove the charges against the actor on all counts.
Salman was found guilty by a sessions court on May 6 last year and convicted for, among others, culpable homicide not amounting to murder, and sentenced to five years in jail for the accident which killed one man and injured four others. All victims were sleeping on the pavement.
Salman also denied he was drunk at the time of the accident, saying he was keeping away from alcoholic beverages in preparation for the shooting of the film "Garv".
Telling the apex court that the accident took place as the left front tyre burst resulting in the vehicle spinning out of control, Salman said driver Ashok Singh was driving towards his home at 40-50 km an hour from JW Marriott to Hill Road.
At the time of the accident, Salman said some repair work was going on near the junction, as a result of which there were stones and rubble lying on the road.
"When the vehicle approached the junction of St. Andrew's Road and Hill Road, the left front tyre of the said vehicle burst, due to which the said vehicle swerved sharply to the left.
"Ashok Singh tried to apply the brakes and tried to control the vehicle but by then (it) climbed the stairs and came onto the platform outside the American Express Laundry, hit the shutter and stopped," he said.