The officer, identified only as V53, told an inquest into Mark Duggan's death that he thought he was brandishing a gun.
The 29-year-old father of four was shot when the taxi in which he was travelling was stopped by armed police in Tottenham, north London in August 2011.
Two days after he died, Tottenham exploded into violence that spread across the capital and then on to Birmingham, Manchester and other cities in England. Five people died in the violence.
Several of Duggan's relatives attended the second day of the inquest, including his aunt Carole Duggan who wore a black t-shirt bearing the slogan "time for truth and justice".
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A lawyer acting for the inquest, Ashley Underwood, told the jury that when his taxi was stopped: "Mr Duggan wasn't shocked into submission, he got out of the minicab and he ran.
"You will hear from V53 that he was running with a gun in his hand and he started to bring the gun into the aim."
But the jury also heard that a loaded gun wrapped in a dark sock was found several metres from the site of the shooting, and that Duggan may have been holding a mobile phone in one hand just before he was killed.
No weapon was found on Duggan's body.
Underwood told the jurors that they will need to address whether the police operation that ended in Duggan's death was planned and carried out in a way that minimised the need to use lethal force.
Police had trailed Duggan from a housing estate after receiving information that he had picked up a firearm.
The jury was told that the case has been complicated by an anonymous note sent last year to a number of people including Duggan's family and the Metropolitan Police Commissioner.
It claimed that a police informant had told his handler he could persuade Duggan to pick up the gun, allowing officers to arrest him.