Addressing protests over minorities killed by police officers, President Obama said racism is “deeply rooted” in the U.S. and that activists should keep pressing steadily in their demands for reform.

“This is something that is deeply rooted in our society, it’s deeply rooted in our history,” Mr. Obama said in an interview with BET, a portion of which was released Sunday. “When you’re dealing with something as deeply rooted as racism or bias … you’ve got to have vigilance but you have to recognize that it’s going to take some time, and you just have to be steady so you don’t give up when we don’t get all the way there.”

Mr. Obama held meetings at the White House last week with young civil-rights activists who are protesting the shooting death of an unarmed black teenager by a white police officer last August in Ferguson, Missouri.

And on Thursday, after a grand jury in New York refused to indict a white police officer for the choke-hold death of a black man, the president he wants to ensure that law-enforcement officials “are serving everybody equally.”

Demonstrators protested across the nation again Saturday night, in locations including New York City; Seattle; Portland, Oregon; Davidson, North Carolina; and Tampa.

“This isn’t going to be solved overnight,” Mr. Obama said in the BET interview, adding that America has made progress on civil rights over the past 50 years and that he believes the nation will eventually solve its problems with racism.

“As painful as these incidents are, we can’t equate what is happening now to what was happening 50 years ago,” the president said. “If you talk to your grandparents, parents, uncles, they’ll tell you that things are better — not good, in some cases, but better. We have to be persistent, because typically progress is in steps. It’s in increments.”

Mr. Obama’s comments come as a new Bloomberg Politics poll found that a majority of Americans, 53 percent, say the interactions between the white and black communities have deteriorated since he took office. Among white people, 56 percent said relations have worsened; 45 percent of blacks feel the same way.

The survey on Sunday showed that 36 percent of Americans believe that race relations have stayed the same under Mr. Obama’s leadership, and only 9 percent believe relations have improved.

The poll also showed wide disparities by race over the New York and Missouri cases. Ninety percent of blacks in the poll said the grand jury in New York was wrong not to indict the officer in the chokehold death of Eric Garner; 52 percent of whites believed the officer should have been indicted.

In the shooting death of Michael Brown in Ferguson, 89 percent of blacks disagreed with the grand jury’s decision not to indict the police officer. But 64 percent of whites agreed with the grand jury’s decision.

The president has resisted calls from some civil rights leaders to visit Ferguson. Instead, last week Mr. Obama held a series of meetings Monday with Cabinet members, community representatives and young activists at the White House, and he announced the creation of a task force to develop recommendations for improving relations between law enforcement agencies and minority communities.

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