Speaking on the Tonight Show Starring Jimmy Fallon, the actor pointed out that his six children are all mixed race.
“My children are all half black and I don’t have, even me, I take certain things for granted,” De Niro said in reference to having more opportunities as a white man.
“When people say that they tell their kids, ‘Keep your hands [out] when you’re stopped by any cops, keep your hands on the steering wheel, don’t make a sudden move, don’t put your hands below, don’t do this,’ you understand that.
“That’s scary,” the 76-year-old added. “That has to change.”
The actor went on to talk about police brutality and the protests that have arisen as a result of George Floyd’s death.
Mr Floyd was killed last month after police officer Derek Chauvin knelt on his neck for almost nine minutes. Mr Chauvin has been charged with second-degree murder and manslaughter.
“Anybody who hurts another person for no reason other than self-defence or the defence of other people around shouldn’t be doing that job,” De Niro said.
The actor has two children with his ex-wife, Diahnne Abbott, Drena, 48, and Raphael, 44.
He has twin sons, Julian and Aaron, 24, with his ex partner, Toukie Smith; and one son Elliot, 22, and daughter, Helen, eight, with his ex-wife Grace Hightower.
The actor previously spoke to People about how he would encourage his children to pursue acting careers if they wanted to.
“For my kids, I tell them, ‘If you want to be an actor or you want to do this or that, that’s fine as long as you’re happy,” De Niro said at the time. “Just don’t sell yourself short. That’s the most I would say — push yourself a little more and reach for what you really think it is you want to do. Don’t be afraid.”
He added: “It’s important for them to find their own lane.”