For weeks, New York City has been the roiling epicenter of a national reckoning over the police and race, attracting nightly protests since a Staten Island grand jury declined to bring criminal charges against a white police officer in the case of Eric Garner, an unarmed black man who died after a chokehold in July.

Police union leaders have condemned the mayor for what they have called insufficient support of the police; they have circulated a letter allowing officers to request that he not attend their funerals in the event of a line-of-duty death.

At the news conference on Saturday, at Woodhull Hospital in Brooklyn, the mayor tried to deflect focus on the recent tensions. He said it was “a time to think about these families” and not “a time for politics or political analysis.”

Asked on Saturday about the turned backs and union messages, Phil Walzak, the mayor’s press secretary, said it was “unfortunate that in a time of great tragedy, some would resort to irresponsible, overheated rhetoric that angers and divides people.”

During the briefing, Mr. de Blasio largely deferred to Mr. Bratton. The mayor recalled the emotional scene with the families of the officers, Wenjian Liu and Rafael Ramos, at the hospital. The 13-year-old son of Officer Ramos, the mayor said gravely, “couldn’t comprehend what had happened to his father.”