Thursday’s killing is the sixth such incident in recent months, said police.
Riad Khalas Abd Allah, 25, was driving at a normal speed 150 metres from one of a series of US checkpoints around the heavily guarded main square when the soldiers opened fire, said Police Major Adnan Muhammad Sadr.
His vehicle turned up no weapons and no explosives, said the major in the US-trained police.
The death happened during heavy rain which had apparently diminished visibility.
But Sadr, who heads the local police station, said there had already been five previous fatal shootings by US troops in the same square.