NEW YORK—Confronting the first civil rights test of his administration, Mayor Bill de Blasio is struggling to take command of a controversy over the police and race that has pitted his longtime liberal supporters against the police department he now depends on to keep the peace.Mayor de Blasio had hoped for a healing moment two weeks ago at City Hall, gathering police officials, clergy members and social activists to show that New Yorkers could unite in the aftermath of a Black Staten Island man’s death in police custody. But the event quickly turned into a spectacle. Rev. Al Sharpton, unaware that he would be asked to share the stage with William J. Bratton, the police commissioner, delivered a provocative attack on law enforcement as Mr. Bratton sat stone-faced, inches away. With Mr. Sharpton to this left and Mr. Bratton to his right, Mayor de Blasio sounded more moderator than mayor, taking pains to mollify both. It hasn’t worked. By Wednesday of last week, as police unions threatened a slowdown, Mr. Sharpton and scores of liberal activists were making plans to ratchet up pressure on City Hall, hoping to force an end to the so-called broken-windows approach to policing—cracking down on little crimes to deter bigger ones--that Mr. Bratton pioneered and that Mayor de Blasio has so far defended. “We need to really step up on this,” Mr. Sharpton told the group. Now, Mayor de Blasio is turning to his closest advisors, including the strategists who guided his mayoral campaign and crystallized his position against stop-and-frisk tactics, to help him better communicate his message. “We don’t want to give the wrong answer,” said Rachel Noerdlinger, who like other City Halls aides interviewed for this article said the mayor was carefully trying to articulate a path toward improved relations between the police and the community. “We want to make sure that whatever reform is made is fair and here to stay.” The issue is an important and delicate one for Mayor de Blasio, not least because of the promises he made during last year’s mayoral race, when he burst into the political arena as a feisty critic of aggressive policing and made his teenage biracial son a symbol of his opposition to the stop-and-frisk tactic. As the city’s chief executive, Mayor de Blasio has had to muffle his inner advocate, aware that critics will pounce on any suggestion that he is undermining law enforcement. But to many of the reformers who once marched beside Mayor de Blasio, the mayor’s cautious, middle-ground approach--after the death of Eric Garner last month is what appeared on a video to be an illegal police chokehold--has been interpreted as weak. “Now is not the time to talk about nuance on broken windows after a coroner has ruled that a man has been murdered on the street in broad daylight,” said Christina Greer, who teaches political science at Fordham University. “People don’t want to hear that right now.” Mr. Sharpton, who declined to endorse a Black candidate, William C. Thompson Jr., over Mayor de Blasio in last year’s Democratic primary, said in an interview that he is now hearing from disgruntled ministers and community leaders who have questioned the mayor’s commitment. “What’s he going to do?” is the question that Mr. Sharpton said he hears the most. As activists fret, policy officers have grumbled, with many at Police Headquarters surprised to see Mr. Sharpton, at the other week’s round table, accorded a position of prominence equal to Mr. Bratton. “We protect Al Sharpton’s right to have his opinion, but his opinion should not be elevated,” Patrick J. Lynch, president of the Patrolmen’s Benevolent Association, said on “NY1” Wednesday night. Mayor de Blasio’s aides said the external pressure was exactly why the mayor had remained circumspect on the Garner episode, saying Mayor de Blasio did not wish to be baited by either side. “We’re focused on the long game and that means real, lasting change,” said Peter Ragone, a senior advisor. “That’s going to take more than one or two news cycles.” The mayor’s public remarks have echoed that thought. “We’re on a much bigger track here. We have bigger work to do,” Mayor de Blasio said this week, asked if he was worried about the state of police-community relations in the city. “I don’t get lost at any moment in the public debate. And I don’t let any one voice pull me away from my vision.” That vision remains vague, leaving Mayor de Blasio’s aides fending off critics who fear he will not come through with a forceful reworking of the Police Department’s approach. “Everybody is acting like he’s unbendable,” said Ms. Noerdinger, who worked for Mr. Sharpton before she joined City Hall. Behind the scenes, however, mayoral aides have watched some of their efforts go awry. Mr. Sharpton said he was initially told that last week’s City Hall event would be a private gathering with Staten Island community members. He arrived to discover that Mr. Bratton—and a phalanx of television cameras—would be in the room, too. With the public watching, Mr. Sharpton said he felt compelled to deliver his full-throated critique of the police department. The event’s key image--Mr. Bratton, Mayor de Blasio and Mr. Sharpton sitting beside one another—was seized on by administration critics and showed up on the cover of the next day’s New York Post, with the headline, “Who’s the Boss!” The administration has pledged to retrain police officers in handling arrests, but some activists have dismissed that as lip service. “The response from the commissioner is that we need more training,” said Javier Valdez, an advocate for immigrants. “Training without accountability doesn’t go far.” Mr. Valdez recalled how Mayor de Blasio’s aides reached out in the wake of Mr. Garner’s death. “They wanted us to know they were on top of it,” he said. But as advocates began to intensify their calls for an end to the broken-windows strategy, those conversations grew more adversarial, if still respectful. “To their credit, they have not tried to stop it,” Mr. Valdez said of the administration. “They have tried to see what the best way forward is.” He added: “We’re not there yet. We feel that broken windows needs to change drastically and the commissioner and the mayor feel a different way.” In the days ahead, Mayor de Blasio’s team is hoping to remind New Yorkers of the mayor’s other efforts toward racial equity, such as settling a lawsuit from the Central Park Five and installing as police commissioner Mr. Bratton, who has agreed to continue the downward trend in stops and frisks. Last week, however, the mayor’s profile in the city has been low. He decamped to Washington on Tuesday for a White House dinner with African heads of sate—after sending his regrets that he could not visit local police precincts for the National Night Out Against Crime. Last week, the mayor spent the morning in Washington meeting with the federal housing secretary. He had no question-and-answer session planned for his Thursday schedule.