The coronavirus pandemic in America’s hardest-hit state is starting to wane, its governor said, as more U.S. protesters rallied to lift social-distancing restrictions.

New York Gov. Andrew Cuomo said at news conference Saturday the number of people currently hospitalized in the state for Covid-19 was below 17,000 compared with about 18,000 at its peak.

With more than 235,000 reported coronavirus cases, New York accounts for about one-third of all infections in the U.S., according to data compiled by Johns Hopkins University. It has nearly three times as many as the No. 2 state, New Jersey, despite a population just over twice as large.

But the average person with Covid-19 in New York now infects 0.9 other people, compared with 1.4 at the height of the outbreak, according to Mr. Cuomo, indicating that the virus’s spread is slowing.

“You could argue that we are past the plateau and we are starting to descend,” the governor said.