NEW YORK >> The critical indicators surrounding the coronavirus crisis in New York have clearly turned a corner: Deaths have slowed to a trickle, new cases have declined sharply and the numbers of hospitalizations and intubations have eased.

But over the weekend, a more ominous sign emerged. Throughout New York City, many people openly disregarded social-distancing rules, prompting state officials to threaten to reinstate restrictions in the city to guard against a second wave of infections.

“We have 22 states where the virus is increasing,” Gov. Andrew M. Cuomo said at a news conference today. “It’s a dramatic national turnaround. We don’t want the same plight of these other states.”

Cuomo sounded the alarm after a weekend’s worth of videos and reports of people violating social-distancing rules, including on Friday in Manhattan’s East Village and on Saturday in Hell’s Kitchen, neighborhoods with many bars and restaurants.

The governor singled out bar owners and patrons in Manhattan and the Hamptons on Long Island for flouting the rules, and he warned that if local officials did not crack down on such behavior, the state authorities might suspend or roll back reopening plans for those areas.

Such a move could be financially devastating for business owners who were forced to close for most or all of New York’s almost three-month shutdown, and for the tentative recovery in the city, where municipal coffers were decimated as nearly 1 million people lost jobs.

“There is a very real possibility that we would roll back the reopening in those areas,” Cuomo said Sunday, suggesting that a second wave of infections was almost inevitable if people gathering outside bars and others violated rules. “It will come. And once it comes, it’s too late.”

Cuomo’s warning came as state officials touted the minuscule rate of new positive virus cases in New York — just over 1% of more than 56,000 tests conducted on Sunday, according to the governor — and as other states grappled with surges in infections.

The number of virus cases has been rising in many of the states that reopened earlier, and in a broader fashion, than New York: Arizona, Florida and Texas all recently reported their highest numbers of cases yet. The governors of Oregon and Utah have taken the drastic step of pausing reopenings in their states as a result of similar spikes.

Without a vaccine for the virus, experts have warned, about 70% of the population will need to be infected and develop immunity to halt the spread of infection. New York has had about 390,000 confirmed cases, or about 2% of the state’s population.

As of today, about 1,600 people in the state were hospitalized because of the virus, the fewest since March 20 and a huge decline from a peak of over 18,000. The daily death toll has hovered below 50 for the past five days, compared with the nearly 800 in one day that were recorded at the outbreak’s peak.

But health officials have cautioned that the number of cases could rise as businesses fully reopen, people return to work and commuters take mass transit again, especially in New York City, which has tallied more than 20,000 virus-related deaths. The city began a limited reopening on June 8 that allowed construction and manufacturing to resume, while also permitting curbside and in-store pickup for retail businesses.

Another concern is the recent mass protests against police brutality that have, at times, clogged the city’s streets with tens of thousands of people. Although they have encouraged participants to wear masks, Mayor Bill de Blasio and Cuomo have fretted about the possibility the protests could fuel the virus’ spread.

There have also been conflicting messages from the state leaders about social gatherings. Such gatherings are still technically limited to 10 people, although Cuomo said today that the New York regions in the third phase of reopening — most of the state from the Hudson River to Lake Erie — could allow gatherings of up to 25 people.

The mixed messages on gatherings, along with a weekend of warm weather, may have contributed to a false sense of security among those who were seen flouting social-distancing guidelines.

On Sunday, Cuomo said that the state had been deluged with around 25,000 complaints about businesses that were “in violation of the reopening plan.” He warned that bars and restaurants could lose their liquor licenses if they failed to comply, noted that state Liquor Authority inspectors had been dispatched to problem areas and said that he had called several establishments himself.

But he emphasized it was ultimately up to local governments to enforce the state’s reopening policies, and he publicly urged mayors and county executives to target establishments that were found to be flouting rules.

“They don’t want to enforce them because they’re not popular,” Cuomo said today. “Nobody wants to go to a bar and say, ‘You guys have to wear a mask. You guys are violating social distancing.’ I get it, but they have to do their job.”

A spokeswoman for de Blasio, the governor’s fellow Democrat and frequent rival, took issue with Cuomo’s remarks, saying in a statement that city employees had worked over the weekend to disperse large groups, distribute face coverings and help business owners keep patrons at an appropriate distance from one another.

“We must balance safety with people’s need to reopen their businesses,” the statement said. “These businesses are allowed to be open per the governor’s guidelines, and we don’t believe imprisoning people or taking away their livelihood is the answer.”

In another sign of frustration over the virus-related restrictions, residents of Brooklyn’s Williamsburg neighborhood gathered at a playground there today to demand that it be reopened so children who had been cooped up for months had a place to play.

Joseph Lentol, a state assemblyman who represents the area, said police officers from the local precinct had provided a temporary reprieve by unlocking the playground’s gates. Lentol said he understood the need for rules meant to keep the virus contained, but suggested that there were inconsistencies in how they were being enforced.

“Nobody seems to be disciplining people who go out and stand around all night in the street and drink,” he said.

Today was also the start of the second stage of New Jersey’s reopening. Across the state, outdoor dining was allowed to resume with restrictions, and retail businesses opened their doors for limited indoor shopping for the first time in months.

“Our goal is to not experience the spikes that other states are now seeing because they rushed to open too much, too soon,” Gov. Philip D. Murphy said. “We have lost too many lives in too short a period to not heed the lessons of this virus.”