Mayor Bill de Blasio swept to victory last year with a promise to salve the wounds of New Yorkers who distrusted the police. His critics warned that crime would soar again.

So far, neither has happened.

Now, as protests over the Eric Garner case course through New York City and beyond, Mr. de Blasio’s pledge to bridge the police-community divide has become, with escalating urgency, perhaps the foremost challenge of his mayoralty. It is a cause with an audience from Ferguson, Mo., to Capitol Hill to the city police precincts, where some rank-and-file officers remain wary of the mayor’s calls for reform.

On Thursday, he outlined a series of planned changes in police training, a day after a Staten Island grand jury declined to indict a white police officer who in July performed a chokehold on Mr. Garner, an unarmed black man who died after the confrontation.

The police will be taught strategies to control ego and adrenaline and urged to suppress profanity, city officials said. Officers will be exposed to the culture of the communities they are asked to patrol and given new guidance on how to persuade suspects to comply with arrest without the use of force.