Alton Sterling, a 37-year-old black man, was shot during a scuffle with two white police officers in the car park of a convenience store in Baton Rouge.
Officers were called to the scene following an anonymous report from someone claiming they had been threatened by a person who had a gun.
One police official said Mr Sterling was carrying a gun at the time, however, shocking video footage of the incident which surfaced on the internet does not clearly show whether there was a firearm in his hand or whether he was reaching for one.
The father-of-five's death prompted angry protests among the black community of Baton Rouge, with attendees at Wednesday's vigil calling for justice.
A civil rights investigation by the US Justice Department will now examine whether police used unreasonable or excessive force against Mr Sterling.
Bishop Dr Joe Aldred, who is responsible for Pentecostal and Multicultural Relations at Churches Together in England, told Premier's News Hour programme he is shocked such an incident can happen in 2016.
He added: "My mind goes back, when I hear about this and when I see the over-spilling of anger, particularly in the moment of Alton Sterling's killing ...to the troubled nature of the relationship between black and white in the Deep South.
"I know this is under investigation so one has to be a bit careful about what one says but what I see is that somebody is pinned down on the ground and then killed whilst he's on the ground, under the complete control of two officers."
Describing the shooting as a tragedy, Democratic presidential candidate Hillary Clinton called for the rebuilding of trust between police and the communities they serve.
She said: "Something is profoundly wrong when so many Americans have reason to believe that our country doesn't consider them as precious as others because of the colour of their skin."
Similarly, Baton Rouge Police Chief Carl Dabadie Jr branded the incident a "horrible tragedy" and said officers don't yet fully understand what happened.
"Like you, there is a lot that we do not understand. And at this point, like you, I am demanding answers," Mr Dabadie said.