The city will impose a 60-day limit on how long families with children can stay at any one shelter before having to leave and reapply to enter the system.
The letter, responding to New York City’s list of demands for state help, said the city had already rebuffed some of the state’s offers and had been slow to help migrants.
As migrants sleep on sidewalks outside a Midtown hotel, the city is struggling to avoid a homelessness crisis that resembles Los Angeles’s or San Francisco’s.