A supporter of the NAACP raises his hands in solidarity while marching past a burned building in Ferguson, Mo., on Nov. 29. (Adrees Latif/Reuters)

Meeting with a group of young minority leaders in the Oval Office on Monday afternoon, President Obama invoked a simple phrase to describe his approach to improving the often difficult relationship between police officers and people of color: “Better is good,” the president said.

“When I hear the young people around this table talk about their experiences, it violates my belief in what America can be to hear young people feeling marginalized and distrustful, even after they’ve done everything right. That’s not who we are,” Obama told reporters after the meetings. “And in the two years I have remaining as president, I’m going to make sure that we follow through, not to solve every problem, not to tear down every barrier of mistrust that may exist, but to make things better.”

The youth leaders said they urged Obama to discuss these tensions in a bolder way.

“People want the president to be out front the same way he did with immigration, gay rights and women’s rights. They want him to make this an American issue,” said Howard University student body president Leighton Watson, who met with Obama. “The consensus from everyone — the students and the mayors — was that we wanted the president to be more out in front in a visual and audible way. We don’t question his commitment. We just want him to continue it in a way people can feel.”

The unusual gathering, wedged between a meeting with Cabinet members and a session that the youths also attended with established civil rights leaders, elected officials, law enforcement officials and faith leaders, spoke to the challenge Obama continues to face on the issue of race relations. Eschewing a high-profile televised address or a speech in Ferguson, Mo. — which has been roiled by the killing of Michael Brown, an unarmed, black 18-year-old — Obama has focused on crafting a handful of discrete policy initiatives and speaking in measured terms about the frustrations of many African Americans.

On Monday, he established a task force to modernize policing policies and ordered federal authorities to impose modest restrictions on a controversial program providing military equipment to local law enforcement, his first formal policy response to the crisis.

The president made the same case for incrementalism behind the scenes, according to a senior administration official who participated in the session, telling the young leaders that they should not give up on their activism but that they need to recognize policy change can be slow. But he also emphasized that he recognizes what they have experienced, because he had experienced racial profiling himself.

“He offered us a lot of encouragement with his background as a community organizer, and told us that even incremental changes were progress,” said Brittany Packnett, the executive director of Teach for America St. Louis. “He didn’t want us to get discouraged. He said, ‘Keep speaking truth to power.’ ”

The youth activists spent about 45 minutes with Obama in the Oval Office. With just a handful of youths in the room, “we really had rich perspectives to share,” Packnett said. “He wanted to hear our personal perspective.”

“We walked out of the meeting thinking that was a step,” Packnett said, “a step in the right direction”

Afterward, Obama told reporters that he realizes there have been presidential commissions and task forces in which “nothing happens.”

“What I try to describe to people is why this time will be different,” he said. “And part of the reason this time will be different is because the president of the United States is deeply invested in making sure that this time is different.”

Still, some blacks, as well as a majority of whites, are dissatisfied with Obama’s handling of the incident in Ferguson, according to a new Washington Post-ABC News poll. The survey finds that most Americans, 52 percent, disapprove of how the president has handled the episode, compared with 39 percent who back his approach. The poll shows the country evenly divided on whether a St. Louis County grand jury did the right thing in deciding not to indict police officer Darren Wilson in Brown’s shooting, with 48 percent approving of the decision and 45 percent disapproving.

Respondents were just as divided on the question of whether the federal government should pursue civil rights charges against Wilson; 48 percent said it should, while 47 percent said it should not.

Rep. Emanuel Cleaver II (D-Mo.) said Obama’s blackness actually presents problems for him.

“I think he has walked between the raindrops as well as anyone in his position could possibly do,” Cleaver said in an interview Monday. “There are African Americans who would like for him to sound Eldridge Cleaver and H. Rap Brown. I would say to those people, you have created an unrealistic expectation out of a man who has to govern and work with people whose views on race might not be as sophisticated as he might like, but he’s got to work with them anyway.”

But others are more critical. Khalil Gibran Muhammad, author of “The Condemnation of Blackness: Race, Crime, and the Making of Modern Urban America,” said that at times Obama has spoken more passionately about the rights that immigrants and gay and transgender Americans should enjoy than those of African Americans.

“He has not been willing to mount the kind of policy and societal critique that even [Attorney General Eric H. Holder Jr.] has been willing to do,” Muhammad said. “He uses himself as a symbol of progress while both acknowledging the frustration that others have and, to some extent, chastising it.”

On Monday, the White House honed in on the criminal justice system, which has emerged as a focus in the national debate over civil rights and the protests in response to Brown’s shooting. The president convened a Cabinet meeting with heads of the agencies involved in the military equipment program, directing them to take steps to ensure there is greater coordination, to review how the equipment is distributed to and used by local law enforcement, and to report back in 120 days.

He also proposed spending $263 million over the next three years on body cameras that can be worn by police and better training for law enforcement agencies.

The president also established the “Task Force on 21st Century Policing,” which will be chaired by Philadelphia Police Commissioner Charles H. Ramsey and Laurie Robinson, a professor of criminology, law and society at George Mason University.

Nicholas Turner, president of the New York-based Vera Institute of Justice, said the new policies made sense because the U.S. criminal system is so decentralized and congressional approval would be required for many other changes. The White House, Turner said, “has an important role as educator in chief, surpassing its ability to change policies and practices largely governed at the state and local level.”

During his daily briefing, White House press secretary Josh Earnest sought repeatedly to cast the Ferguson issue in broader terms than just race.

“This goes to sort of the foundational relationship, again, between law enforcement agencies and the communities that they’re sworn to serve and to protect,” he said.

But in many ways, the intersection of race and class is a central question in how citizens in Ferguson and elsewhere interact with the police. Laura W. Murphy, who directs the American Civil Liberties Union’s Washington legislative office and met with Obama on Monday, praised the president for proposing “a robust set of policies to respond to the problems of racial profiling and use of excessive force.”

But she said the administration could go further by finalizing an update of the Justice Department’s 2003 “Guidance Regarding the Use of Race by Federal Law Enforcement Agencies” and withholding federal funds from local law enforcement entities that flout civil rights protections or provide inadequate training for their officers.

“I don’t think the president is unaware or insensitive in any way,” Murphy said. “I do think there are a mixture of opinions in his administration about what actions he should take.”

One remaining question is whether Obama will visit Ferguson. Earnest said that no decision had been made but that the president “recognizes that not just one presidential trip to Ferguson is going to solve the problem here.”

Cleaver said he did not think Obama should travel there. “The president going to Ferguson might change the debate from the needs in that small town to a debate over whether the president should have gone there,” he said.

The Post-ABC poll was conducted Nov. 25 to 30 among a random national sample of 1,011 adults reached on conventional and cellular phones. Overall results have a margin of sampling error of plus or minus 3.5 percentage points.

Scott Clement and Peyton Craighill contributed to this report.

Body cameras for police: See video of the president’s comments at wapo.st/ObamaPolicePackage.