Crime is a vulnerability for any mayor. It has been particularly so for Mr. de Blasio. He has at times found himself at odds with rank-and-file police officers as his administration has sought to win trust in minority communities often most ravaged by violence.

This year, officers have stepped back from some areas of policing, particularly with regard to marijuana possession and some other low-level offenses. They have logged hundreds of thousands fewer stops, summonses and arrests than in previous years. Mr. Bratton, the nation’s pre-eminent practitioner of so-called quality-of-life policing, has called the drop in police activity a “peace dividend” gained from low crime and paid to average New Yorkers.

Whether that approach could be sustained amid increases in violence is a question increasingly being put to the mayor and police officials, who were asked repeatedly on Monday whether they were considering ramping up street stops.

“If we see an area where there is an increase in violence, of course we’re going to put more resources in there,” Chief O’Neill said. “But the stops that we want are good stops.”

Officers on the street have said that those who might choose to carry a gun are now more emboldened to do so. Indeed, police officials on Monday suggested that it was a daily occurrence that routine street stops by officers — for offenses like drinking in public and double-parked cars — have turned up guns.

At the same time, the number of guns seized from the street has declined roughly 20 percent over the last five years. The police recorded 3,648 guns recovered during arrests in 2010. By 2014, the police recovered 2,942 guns.

So far this year, the number is flat, officials said on Monday.

At a similar briefing with reporters last month, officials stressed the high concentration of homicides in particular precincts, especially in Brooklyn and the Bronx. Mr. Bratton sought to put the increases in historical context, and emphasized the nature of both the victims and the known perpetrators.