Many people have been aghast at the video posted live online by the victim’s girlfriend as he lay dying.
Philando Castile, 32, was shot by a police officer after a traffic stop at Falcon Heights near Minneapolis.
It sparked protests outside the Minnesota governor’s headquarters. President Obama said on his Facebook page that he and his wife shared people’s “anger, frustration and grief”.
Castile’s girlfriend who had published the live video of the aftermath, addressed the crowd.
“Not one shot, not two shots, not three shots, not four shots … but five shots. For no reason,” Diamond Reynolds said.
Castile, who was driving the car carrying Reynolds and her four-year-old daughter, was shot by her account after police pulled their car over for a broken tail light.
Reynolds said Castile had a gun but was reaching for his driving licence when he was shot.
Her video showed a police officer outside the car pointing a gun. Reynolds described what was happening, speaking calmly but sometimes emotionally to the police officer, as she feared Castile was dying.
Minnesota’s Governor Mark Dayton called on the US Justice Department to investigate. A state inquiry was announced earlier.
“Would this have happened if the driver and the passengers were white? I don’t think it would have,” he told reporters. “So I’m forced to confront that this kind of racism exists, and it’s incumbent upon all of us to vow and ensure that it doesn’t happen and doesn’t continue to happen.”
“I promise I will do everything and my administration will do everything in our power to see this matter brought to justice. And that all avenues are pursued to do a complete investigation,” he said.
In Louisiana several hundred people gathered at the spot outside a food store in Baton Rouge where Alton Sterling was shot dead by police the previous day.
Video appeared to show him being pinned to the down and shot several times at close range.
Two more fatal shootings by police of African Americans in two days – both scenes posted on social media – have sparked peaceful but powerful protests.