A new task force will address street homelessness block by block and have the capability to send teams on scene within an hour of a resident reporting a homeless person, New York City Mayor Bill de Blasio said on Thursday.

The mayor described the effort in remarks to a business group, just days after he announced the resignation of the homeless-services commissioner and said City Hall would conduct a top-to-bottom review of the city’s work on homelessness.

The initiative marks one of the most visible moves by Mr. de Blasio to address homelessness, which has become an increasingly intractable political problem for the mayor.

There are more than 58,000 people in shelters, but the specific target of the new effort is the homeless on the street, who the mayor said can “make many New Yorkers uncomfortable, and even fearful.”

The initiative will be known as NYC Homeless Outreach & Mobile Engagement Street Action Team—or HOME-STAT, Mr. de Blasio explained in a breakfast speech to the Association for a Better New York.