The number of patients hospitalized with the coronavirus in New York State rose on Wednesday by only 200 from the previous day, officials said on Thursday, the smallest increase since before the imposition of a statewide lockdown and another promising sign that the government’s measures may have started working.

But even as the flow of infected people into emergency rooms appeared to level out, more than 18,000 ailing patients — nearly equal to the capacity of Madison Square Garden — were still packed into New York’s hospitals, and the daily death toll was near 800 for the second day in a row, bringing the state’s total fatalities to more than 7,000.

For the better part of a month, the residents of New York, which has more than one-third of the total cases in the United States and more cases than any other country, have pored over data on the outbreak, trying to determine if the curve of new infections had finally been flattened and if the apex of the crisis had been reached.

While elected officials warned on Thursday that no one — not even the analysts who had built the statistical models — could perfectly predict what was ahead, there were fragile indications of good news on the ground as doctors in New York said the crush of new patients had started to slow down and the atmosphere of panic in their hospitals had begun to subside.