CCTV footage appears to show Michael Brown, 18, stealing from a convenience store and intimidating the owner.
Michael Brown’s family denied their son was “perfect” but criticized what they see as a police attempt to “justify the execution-style murder”.
The killing sparked days of angry clashes between police and protestors.
“Stay with us, we don’t want to see any violence on the streets. Please continue to peacefully protest,” said Michael Brown’s cousin, Eric Davis.
There were no reports of unrest for a second successive evening on Friday, as a few hundred people demonstrated quietly at a filling station, which was looted and burnt last weekend.
Civil rights leader Al Sharpton says a rally, led by Michael Brown’s family is planned for Sunday.
“The family has never said that Mike Brown was perfect,” said a lawyer representing the teenager’s family.
Ferguson Police Chief Thomas Jackson said the officer who shot Michael Brown, later identified as Darren Wilson, did not know that he had allegedly stolen goods from a nearby store.
“The initial contact between the officer and Michael Brown was not related to the robbery,” Thomas Jackson said.
Instead, he added, the reason for the stop was that Michael Brown “was walking down the middle of the street stopping traffic”.
Thomas Jackson said he had released the footage of the crime only because he had been forced to do so because of numerous freedom of information requests from journalists.
He described the robbery at the convenience store as being committed without the use of a weapon.
CCTV pictures in a police report show a well-built black man intimidating a clerk in the store.
The police report identifies the man as Michael Brown, described as being 6ft 4in and 292 pounds.
It says he “grabbed a box of Swisher Sweet cigars” and handed them to a second suspect identified as Michael Brown’s friend, Dorian Johnson.
Since the shooting on Saturday, Thomas Johnson has given a number of interviews in which he has said Michael Brown held up his hands in an act of surrender before being shot by the officer.
Also on Friday Thomas Jackson revealed the name of the officer who shot and killed Michael Brown – Darren Wilson – and said he was injured in a struggle with Brown.
Darren Wilson is a six-year veteran of the police force with no disciplinary record, Thomas Jackson said.
Members of the majority black Ferguson community have reacted angrily to the revelations.
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