On Monday, Mr. de Blasio said that the Black Lives Matter movement had “hit the right note.”

“The very phrase ‘Black Lives Matter’ is a necessary part of the national discussion,” he said. “It has helped us to recognize that sadly our history over and over again did not value African-Americans.”

Mr. de Blasio, a Democrat, has not framed the discussion in terms of politics, but if race-related issues continue to fester in the city and elsewhere, it could play to his advantage as he faces re-election in 2017. He could then speak directly to some of the central concerns of black New Yorkers, a key constituency that helped him get elected, while also potentially reassuring other groups anxious about the city’s direction.

“He’s got to watch that he’s on the early stages of his re-election, and I think that he knows that his strongest base remains in the African-American community,” said the Rev. Al Sharpton, who has been a supporter of the mayor. “And if he’s going to maintain that base, he’s got to speak to the issues that concern that base.

But he also said that Mr. de Blasio might have more immediate concerns, since Sunday will be the second anniversary of Eric Garner’s death (Mr. Garner died after being held in a chokehold by a police officer on Staten Island, one of the earliest videotaped episodes that helped prompt the Black Lives Matter movement). Mr. Sharpton said the mayor was undoubtedly bracing for more protests.

“I think that he knows he’s got to get in front of this weekend,” Mr. Sharpton said.

Mr. de Blasio won the Democratic primary in 2013 with strong support from black voters, partly because he promoted the image of his interracial family. While polls show that his approval among whites has slipped considerably since he took office, they also show that black voters continue to back him strongly — even though there, too, he has seen some erosion in support.