Hispanic respondents split the difference, with 43 percent reporting lots of movement toward racial equality and 23 percent saying little to none had been achieved.

The same survey found that more than a third of blacks report being discriminated against on the basis of race in the past year, versus 20 percent of Hispanics and 10 percent of whites. Two-thirds of black respondents and a quarter of whites say blacks are not treated fairly by the judicial system.

Still, nearly three-quarters of blacks and 81 percent of whites say the races get along "very well" or "pretty well." 

President Obama plans to deliver remarks next Wednesday at a ceremony commemorating the 50th anniversary of the March on Washington, which drew a quarter million people to the National Mall in 1963 to call for racial equality.

Earlier this summer, the president spoke at length about the issue of race in America following the verdict in the Trayvon Martin murder trial. Obama compared himself to the Florida teen, and said his death should be put into the context of America's race relations.

“When Trayvon Martin was first shot, I said that this could have been my son,” Obama said.

“Another way of saying that is Trayvon Martin could have been me 35 years ago. And when you think about why, in the African-American community at least, there’s a lot of pain around what happened here, I think it’s important to recognize that the African American community is looking at this issue through a set of experiences and a history that doesn’t go away.”

The president said that blacks experienced, on a daily basis, the manifestations of prejudice.

“There are very few African-American men who haven't had the experience of being followed in a department store,” he said. “That includes me.”