Minneapolis police officers will not face criminal charges in the fatal shooting of an armed man who yelled “Please don’t shoot me” last month as he ran through an alley, prosecutors said Monday.

Body camera footage of the shooting, made public by the mayor of Minneapolis on Sunday night, showed a chaotic foot chase through a neighborhood that ended with the man, Thurman Blevins, fatally wounded. Before the gunshots, one officer repeatedly shouted expletives and told Mr. Blevins to drop his gun. Mr. Blevins yelled “leave me alone” as he ran away.

The videos and the decision not to charge the officers provided new details about a case that has renewed longstanding tensions in Minneapolis over how the police use force and treat black people. The officers in the case are white; Mr. Blevins, 31, was black.

But the video footage did little to change two competing narratives that have emerged since the death of Mr. Blevins on June 23. Some watched the images and saw officers following appropriate procedures as they confronted an armed person who refused to comply with their orders. Others said they saw officers overreacting to a scared man simply trying to get away.