The Chicago Police Department said an officer fired at 37-year-old Harith Augustus about 5:31 p.m. when Augustus reached for his weapon.
The protest ended at about 10:30pm, and officials said the officer involved would be placed on desk duty while the incident was investigated.
Jackson called for video to be released and referenced footage from 2014 that showed a white officer shooting a black 17-year-old, Laquan McDonald, 16 times. The Chicago Sun-Times also identified the man as a barber known as Snoop.
Protesters march to the 3rd District Police Station about 11:30 p.m. Saturday, July 14, 2018 in the 7000 block of South Cottage Grove Ave in Chicago.
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Hours after the shooting, dozens of people gathered to protest the man's death. He would not name the officer who shot Augustus.
Police said the man had been "exhibiting characteristics of an armed person".
"We're pissed off; we're exhausted", community activist William Calloway said on Sunday the day after the shooting and standoff with officers.
Protests rocked the city after the videos were released.
During the protest that followed the shooting, officers pulled people to the ground and struck them with batons.
A brief scuffle broke out between chanting protesters and police officers holding batons. Central time, protesters took to the streets and began shouting "murderers" and obscenities at officers.
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CNN reports that at least four people were arrested.
The protest came amid long-simmering tensions over frequent instances of police shootings and brutality against African-American residents in both Chicago and across the country.
He added that many in the crowd had "a false sense of what occurred".
In a statement, the city's Civilian Office of Police Accountability said it's committed to a thorough, objective and unbiased investigation of the shooting.
Saturday's shooting and subsequent civil unrest come days after a Chicago police officer was filmed telling two young men, "I kill motherf**kers" and threatening to arrest them for walking in the street.
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