SAN FRANCISCO — The city needs about 5,000 additional hospital beds and 1,500 ventilators to face the projected crush of COVID-19 patients in the coming weeks, Mayor London Breed and health officials said Wednesday.

San Francisco now counts about 1,300 medical-surgical beds and 200 intensive-care unit beds at its disposal, said county health director Dr. Grant Colfax. But with 178 identified COVID-19 cases as of Wednesday — and on the heels of the city’s first reported death — the city could soon face capacity difficulties mirroring those of New York City, officials said.

“We are in a better situation than most, but we are still in a situation that requires a significant ramp-up,” Breed said. “It requires the need for our state and federal partners to step up more than they ever have before and to move faster.”

Breed sent a letter to Governor Gavin Newsom and Vice President Mike Pence on Wednesday laying out the city’s needs, she said, including units of personal protective equipment for medical personnel, who are facing a well-documented nationwide shortage of masks, gloves and other items.

Colfax said that the latest bed projections were based off new data from Wuhan, China, as well as Italy and New York.

Despite a joint effort from the city’s hospitals and officials to expand capacity and enforce social distancing, San Francisco could still see its surge capacity “far exceeded” — especially during a so-called second wave of the virus, Colfax said.

Hospitals are working jointly to open up a dedicated floor to treat COVID-19 patients at St. Francis Memorial Hospital, officials said Wednesday. It will include 40 medical-surgical beds and eight ICU beds, with staffing from other facilities, including Dignity Health and Zuckerberg San Francisco General Hospital.

The first 10 beds will open up in early April.

Breed called on San Franciscans to imagine a scenario in which the city had no remaining capacity for hospital beds, asking residents to stay at home unless absolutely necessary.

“We don’t want to get to that point,” she said. “My plea is to ask the public to continue to cooperate, to exercise social distancing, to be responsible for one another, because we’re in this together — we’re all responsible for one another,” Breed said.