New York City has already set up 45 new mobile morgues. Local crematories are now allowed to work around the clock. At one Brooklyn hospital, the in-house morgue was filled to capacity on Tuesday. The next day, the nursing staff ran out of body bags.

As the coronavirus epidemic enters its second month, the casualties in New York are starting to severely tax the city’s ability to accommodate its dead. With more than 1,000 deaths so far and thousands more projected, city officials are working hard to stave off an emergency.

In the past few days, the city’s medical examiner’s office has taken over the collection of bodies, dispatching the fleet of new refrigerated trailers to hospitals in all five boroughs, some of whose morgues have already filled up. Funeral homes are becoming backed up. And, running on smaller staffs, cemeteries and crematories are scrambling to keep up with demand.

“It’s taking longer for the bodies to be released and for the bodies to be transferred,” said Patrick J. Kearns, a fourth-generation funeral director who operates three funeral homes in Queens and one on Long Island. “When you overwhelm the health system, you also overwhelm the death system.”