The victim, believed to be in his 40s, was shot in Romford, east London, on Monday.
Officers received a call at 3.50am about a man making threats who claimed to be in possession of a gun at a property in the area.
Firearms officers attended the address, but were told the man had left.
He was shot at around 4.45am in Collier Row, near Lodge Lane, and was pronounced dead at the scene around 30 minutes later.
A police cordon remains in place in the area and several roads have been closed.
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The Metropolitan Police said: “The Directorate of Professional Standards has been informed.
“A mandatory referral has been made to the Independent Office for Police Conduct.”