Michael Brown, a black teenager, was shot dead by police in Ferguson, Missouri, on August 9.
His father said “hurting others or destroying property it not the answer” in a video posted online.
Michael Brown, 18, was killed by white Officer Darren Wilson following an altercation.
There were more protests overnight and two people arrested as demonstrators gathered outside the police station.
President Barack Obama has joined the calls for calm.
He told ABC News: “This is a country that allows everybody to express their views. Allows them to peacefully assemble, to protest actions that they think are unjust.
“But using any event as an excuse for violence is contrary to rule of law and contrary to who we are.”
Late on Friday, the FBI arrested two men suspected of purchasing explosives for use in protests, CBS News reported.
US Attorney General Eric Holder earlier urged police in the area to show restraint, providing new guidance on how to maintain public safety while protecting free speech rights.
A St Louis County grand jury is currently weighing criminal charges against the officer involved in the shooting. No word has yet been given on when a decision will be announced.
Missouri Governor Jay Nixon has declared a state of emergency in the area and called in 400 National Guard troops in anticipation of protests should charges not be filed in the case.
The case has stoked racial tensions in the US, with many in the African American community calling for Darren Wilson to be charged with murder.
Darren Wilson, meanwhile, has maintained he acted in self-defense.
Initial protests in August turned violent as demonstrators clashed with local police using military-grade riot gear.
6RTlfavKQBQImage source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…