An undeniable part of President Obama’s legacy is that Americans believe race relations have worsened during an eight-year period, with the emergence of the Black Lives Matter movement, assassinations of police officers and several high-profile attempts by the nation’s first black president to bridge the racial divide.

Although Mr. Obama’s popularity is high for a second-term president, polls consistently show the public has a more negative view of race relations today than when he was inaugurated in 2009.

The Pew Research Center reported last week that 19 percent of Americans say race relations are improving, 38 percent say they are getting worse and 41 percent say things are about the same.

A CNN/ORC survey in October found that 54 percent of Americans believe relations between blacks and whites have gotten worse since Mr. Obama became president. An ABC-Washington Post poll in July showed 63 percent of Americans saying race relations were generally bad, compared with 36 percent when Mr. Obama took office.

Minorities are more likely than whites to say race relations are worse. In the Pew poll, 61 percent of blacks and 58 percent of Hispanics said the situation is worse, compared with 45 percent of whites.

“Always when we go through major changes in our society, like the first African-American president, it has a tendency to bring out some of the old problems and challenges of our nation,” said Hilary Shelton, director of the NAACP’s Washington Bureau, who argues that race relations nevertheless have improved overall under Mr. Obama.

On the other side are people such as Milwaukee County Sheriff David Clarke, a vocal supporter of Donald Trump, who criticizes Mr. Obama for hurting race relations and for arguing that America hasn’t overcome the vestiges of slavery and Jim Crow.

“How can the first black president stand up there and try to convince anybody that this country is still racist?” Mr. Clarke said on Fox News. “When many Americans — black, white, Hispanic and you name it — went out and voted for that man and on the way out the door he kicks them right in their teeth, this guy is incredible.”

The president said he doesn’t believe the country is more racially divided and thinks Americans’ expectations were too high for his presidency creating a “post-racial” nation.

“That talk was not only naive, but I think it created some problems down the road,” Mr. Obama said in an interview with NBC anchor Lester Holt. “It meant that African-Americans and other minority groups might have felt as if the problems that had built up over centuries — a wealth gap and an education gap, significant poverty — those things could be addressed overnight.”

He said among some white voters, “there was also maybe an unrealistic notion that somehow, OK, that means discrimination’s over.”

Fair or not, race has been inseparable from discussions about Mr. Obama, including distancing himself from the Rev. Jeremiah Wright in 2008, holding a “beer summit” in 2009 with a white police officer and Henry Louis Gates, the black Harvard professor who was arrested on the porch of his own home, and the president’s observation in 2012 that slain black teen Trayvon Martin could have been his own son.

The president’s decision to insert himself into the Gates episode satisfied nobody. Some critics accused him of undermining law enforcement with his comment that the Cambridge police “acted stupidly,” and black leaders were unhappy that he softened his criticism at the White House meeting with the officer and Mr. Gates.

Public perceptions about race relations nose-dived during the summer of 2014, when rioting broke out after the fatal police shooting of black teenager Michael Brown by a white police officer in Ferguson, Missouri. Other high-profile killings of unarmed minorities by police officers followed, and Black Lives Matter protests erupted in many cities.

Mr. Obama dispatched his attorney general, Eric H. Holder Jr., to Missouri and eventually formed a task force on police practices in an effort to ease tensions. The president met with members of the Black Lives Matter movement, drawing criticism that he was faulting law enforcement.

James Pasco, executive director of the National Fraternal Order of Police, said at the time that Mr. Obama’s comments weren’t helpful to police and that the president “never walked in a police officer’s shoes.” In an interview, Mr. Pasco said tensions still hadn’t diminished.

“There’s certainly been a lot more focus on the rift between the communities and the police who protect them,” Mr. Pasco said. “It’s too early to say who deserves credit or blame for that. I can’t put the blame on the Obama administration when there are so many agitators on both ends of the spectrum trying to exacerbate the problem.”

Last year, 65 law enforcement officers were killed by gunfire, according to the Officer Down Memorial Page. In 2009, that number was 50.

Mr. Pasco said the country still needs “a real dialogue” between police and the communities they serve. With about 18,000 police jurisdictions nationwide, he said, it’s an enormous challenge in which the federal government has limited impact.

“Trump is going to have to confront the same problem that Obama has: the federal government has very little authority over policing at the state and local level,” he said. “The only jurisdiction they do have is to investigate whether there’s cause to believe that wrongdoing was done. That’s not the overarching problem here. The overarching problem is fear and distrust on both sides.”

He said law enforcement officials have “high hopes” for an improved atmosphere with Jeff Sessions as attorney general.

“We have a 25-plus year relationship with Jeff Sessions,” Mr. Pasco said. “We’ve always found him to be supportive of law enforcement and of affording all citizens protections of the law.”

Mr. Shelton, the NAACP official, said that although he believes race relations are “better in some areas” under Mr. Obama, the subject of law enforcement requires more focus in the years ahead. Still, he sees evidence of improved race relations even in the street protests against police brutality.

“If you looked at the diversity of marchers, what you’ll see is the diversity of our young people are gathered together and focused on the same challenge, even when that challenge more specifically affected African-Americans,” he said. “Even though they called them marches for Black Lives Matter, what you saw was great diversities of African-Americans, white Americans, Native Americans, Hispanics, Asian-Americans and others. I think that says a lot about how our nation has come along.”

In his farewell address to the nation last week, Mr. Obama said attitudes about race weren’t going to change completely in eight years.

“If we’re going to be serious about race going forward, we need to uphold laws against discrimination — in hiring, and in housing, and in education, and in the criminal justice system,” he said. “But laws alone won’t be enough. Hearts must change.”

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