And for days, the death toll climbed faster and faster. In New York State, for instance, it rose by more than 200, then by more than 400, then by 630 in a single day.

But on Monday, for the second day in a row, officials found reasons for hope, even as hundreds of people continued to die and thousands clung to life on ventilators.

On both Sunday and Monday, fewer than 600 deaths from the virus were reported in the state: 594 on Sunday and 599 on Monday, Gov. Andrew M. Cuomo said.

New Jersey reported 86 deaths on Sunday and 71 on Monday, after a three-day streak with numbers in the triple digits. In Connecticut, 17 deaths were reported on Monday, the smallest number since last Wednesday.