Attorney Benjamin Crump said the process was “broken” a day after a grand jury opted not to send white police officer Darren Wilson to trial.
Michael Brown was killed on August 9 in Ferguson, Missouri, sparking unrest.
A police chief said violence that followed the yesterday’s verdict was worse than any the St Louis suburb had seen.
More than 80 people were arrested amid riots across several areas of St Louis. Sixty-one of those arrests were in Ferguson, with charges including burglary and trespassing.
Civil rights leader Al Sharpton, who attended a news conference with Michael Brown’s family, criticized the prosecutor’s decision to announce the verdict late at night on Monday, saying it was “irresponsible”.
Al Sharpton said the jury had “broken our hearts” but he vowed to continue “to fight for a new level of accountability of policing in this country”.
Violent protests were not in the spirit of Michael Brown, Al Sharpton added, saying the young man would not “be remembered for the ashes of buildings burning in Ferguson”.
Instead, he said Michael Brown’s family would push for new legislation to protect citizens and support a “Michael Brown law” that required all police officers to wear body video cameras.
Many in Ferguson’s predominantly African-American community had called for Darren Wilson to be charged with murder, but a Missouri grand jury – of nine white and three black members – made no recommendation of charges.
Lawyers for the Brown family criticized the decision to call a grand jury rather than appointing a special prosecutor and accused state prosecutor Robert McCulloch of seeking to “discredit the victim”.
“We could see what the outcome was going to be and that is what occurred last night,” Benjamin Crump told reporters.
“This process is broken. This process should be indicted,” he added.
Missouri Governor Jay Nixon tried to head off further riots on November 25 by ordering National Guard reinforcements to take to the streets of St Louis.
“The violence we saw in areas of Ferguson last night is unacceptable,” Jay Nixon said in a statement.
“That is why today I am meeting with leaders from the Guard and law enforcement to ensure the protection of lives and property.”
Much of the debate since August has centered on whether Michael Brown was attempting to surrender to Darren Wilson when he was shot, but Robert McCulloch said physical evidence had contradicted some of the witness statements.
The jury was made up of 12 randomly picked citizens from the state of Missouri. At least nine votes were needed in order to issue an indictment.
Michael Brown’s family could yet file a wrongful-death lawsuit against Darren Wilson, who is currently on paid leave.
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