President Barack Obama says banishing racism in the US can only happen incrementally, and urged young people to "be persistent" in fighting bias.
He was speaking as protests continue in cities across the US, where thousands have gathered over the past two weeks to condemn a spate of killings of black suspects by white police.
"This isn't going to be solved overnight, this is something that is deeply rooted in our society, it's deeply rooted in our history," Obama said in an interview with Black Entertainment Television that aired on Monday.
He urged young people to press on in their fight against racism, and said patience was crucial.
"We have to be persistent, because typically progress is in steps, it's in increments," he said.
"When you're dealing with something as deeply rooted as racism, or bias, in any society, you've got to have vigilance but you have to recognise that it's going to take some time.
"But we can't just wait for that process to happen on its own," Obama added.
"It also requires policy changes. It requires training. It requires specific steps by police departments, starting from the top, in order to change some of these mindsets."
Obama said race relations had improved over the past 50 years, even though tensions persist.
"If you talk to parents, grandparents, uncles, they'll tell you that things are better, not good in some cases, but better.
"I want my grandsons to be treated like anybody else's grandsons," Obama said.
A series of police killings of African-American suspects in the US has sparked widespread anger and ignited a national debate about race relations and police tactics.
"Part of what I think is so heartbreaking and frustrating for a lot of folks when they watch this is the recognition that simply by virtue of colour you've got less margin for error. And that's particularly true for black boys."
In Ferguson, Missouri, and New York city, two separate grand juries decided not to indict white officers involved in the killing of black suspects, setting off a wave of demonstrations nationwide.
"A country's conscience sometimes has to be triggered by some inconvenience," Obama said, calling peaceful protests "necessary".
"When they turn violent, then they're counterproductive."
Demonstrations were continuing on Monday night in Washington, New York, and Berkeley, a California city where vandalising, looting and clashes occurred over the past two nights. Protests were also scheduled for Los Angeles.
Meanwhile the US Justice Department is announcing new limits on racial profiling.
Except for cases involving terror suspects, federal law enforcement agencies will face a broader ban on controls and arrests based on race, ethnicity, nationality, religion, sex or sexual orientation, officials said.
Attorney General Eric Holder is due to detail the new criteria - which apply to operations involving federal police - on a conference call with local law enforcement leaders, following a revision of the principles set by his predecessor in 2003.
"As attorney general, I have repeatedly made clear that profiling by law enforcement is not only wrong, it is profoundly misguided and ineffective - because it wastes precious resources and undermines the public trust," Holder said in a memo on Monday.
Holder, the first African American to serve as America's top law enforcement official, had promised to take action after a series of incidents in which white police officers went unpunished for killing unarmed blacks.
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