Mayor Eric Adams said on Tuesday that New York City was winning its war against the Omicron surge, noting that the numbers of coronavirus cases and hospitalizations, while still extremely high, have started to drop.

Mr. Adams encouraged New Yorkers to continue to get vaccinated and wear masks.

“Let’s be clear on this — we are winning,” the mayor said at a news conference at City Hall. “We are going to win because we’re resilient.”

Mr. Adams, a Democrat in his third week in office, pointed to the average number of cases recorded daily, which has fallen from a known peak of more than 40,000 to less than 20,000, and to hospitalizations, which have fallen from a daily peak of about 6,500 people hospitalized citywide on Jan. 11 to about 5,800 patients on Jan. 16.

While Mr. Adams has expressed optimism about case numbers and encouraged workers to return to offices, experts say New Yorkers should remain careful. The number of known cases is still much higher than last winter, when there was an average of roughly 6,500 cases a day, according to city data.

During the devastating first wave of the coronavirus in the spring of 2020, testing was scarce, leaving many cases unreported.

New deaths, a lagging indicator, have been increasing, and have averaged about 100 per day in recent days, which is higher than they have been since May 2020.

A wave of Omicron cases may be cresting in the northeastern United States, but the number of virus patients nationwide is at a record high and climbing, overwhelming hospitals whose staffs have been hollowed out by the virus. On Sunday, Dr. Vivek Murthy, the U.S. surgeon general, warned that the Omicron surge had not yet peaked nationally, saying that the next few weeks would be very difficult in many parts of the country as hospitalizations and deaths rise.

“The challenge is that the entire country is not moving at the same pace,” he said.

In her first budget address on Tuesday, Gov. Kathy Hochul also spotlighted the state’s declining case rate and hospitalization numbers. She said the virus positivity rate statewide was now 12.8 percent, about half of what it was on Jan. 2. “We hope to close the books on this winter surge soon,” she said.

Mr. Adams said he was proud that he kept public schools open and that more students were returning to classrooms after widespread absences earlier this month. More than 75 percent of students were in school on Friday, compared to 67 percent on the first day after the winter break.

The city has so far distributed 4.5 million rapid home tests to students, Mr. Adams said. Those tests have identified 25,000 cases.

Mr. Adams suggested last week that he would consider a remote learning option for schools, but his schools chancellor, David C. Banks, said on Tuesday that such an option was not imminent and that it would be difficult to set up.

“It is a big undertaking, even to do it for a short period of time,” Mr. Banks said.

On vaccinations, Mr. Adams said the city had reached a new milestone of 16 million doses administered, including 2.5 million booster doses. But the mayor said New York was still “nowhere near where we need to be” on its vaccination effort.

City data shows that 74 percent of all New Yorkers, and just 47 percent of those between the ages of 5 to 17, are fully vaccinated.