The Central Park tent hospital, in America’s coronavirus epicenter, is the group’s first medical deployment in the United States. While Gov. Andrew M. Cuomo has said that the worst is over if residents remain vigilant, and that hospitalization figures continue to flatten, medical institutions in New York are still struggling to treat critically ill patients in numbers far exceeding typical capacity.

“We will be here as long as we are meeting a need,” said Melissa Strickland, the organization’s communications director.

The 68-bed field hospital in Central Park has 10 I.C.U. beds and ventilators, seven of which were being used at the beginning of this week. The facility had treated 130 patients as of Tuesday, according to the group — a similar number to the Navy hospital ship Comfort, which arrived March 30 and has space for as many as 500 severe coronavirus cases. As of Wednesday, six patients at the field hospital had died.

The clinical staff — more than five dozen emergency response volunteers drawn from the organization’s nationwide roster — work 12-hour shifts. The infection control protocols they rigorously enforce are different and appear stricter than those being used to treat coronavirus patients in American hospitals, where protective equipment has run short, health workers are not always trained to use it, and many have contracted the coronavirus, with some dying. Thus far, Samaritan’s Purse leaders said, none of its workers have fallen ill at the New York field hospital or at a similar one in Cremona, Italy.