After months of promising signs in its fight against the coronavirus, New York State on Monday reported a spike in its rate of new cases, including a rise in New York City and in its northern suburbs.

The rate of positive test results in the city reached 1.93 percent, Mayor Bill de Blasio said on Monday, an increase from the 1.5 percent rate reported by the city a week before, as officials continued to warn about dangerous behavior in several communities.

The increase in the city, the one-time center of the pandemic, and some suburbs contributed to the statewide rate of approximately 1.58 percent — a jump from results reported on Sunday and in prior weeks.

Gov. Andrew M. Cuomo, a third-term Democrat, said on Monday that the increase was primarily because of clusters in Brooklyn, as well as in Rockland and Orange Counties, in the Hudson Valley, saying there was “significant action” in those areas.

Officials are particularly concerned about eight neighborhoods in Brooklyn and Queens, some with large Orthodox Jewish communities, that have accounted for about one-fourth of New York City’s new cases in the past two weeks, despite representing about 7 percent of the city’s population.

On Friday, city health officials began carrying out emergency inspections at private religious schools in some of those neighborhoods, and threatened to limit gatherings or force closings of businesses or schools if there was not better compliance to social distancing requirements.

A continued rise could affect a closely watched plan to reopen the city’s schools: The mayor has said that he will automatically shut down classrooms — which are all slated to be open by Thursday — if the positivity rate exceeds 3 percent over a seven-day rolling average. The mayor has also has twice delayed the start of in-person classes for most students, and on Sunday, the union representing the city’s principals called on the state to take over the reopening effort from Mr. de Blasio.

Mr. Cuomo has previously said that reaching a 2 percent positivity rate would make him “nervous,” and that surpassing a 3 percent rate would cause “the alarm bells to go off.”

On Monday, Mr. Cuomo said that he would make 200 rapid testing machines available to schools and local governments in areas where rates were rising, saying “the key with these clusters is to jump on them quickly.”

All told, the state on Monday reported 834 new cases, out of nearly 53,000 tests, the governor said, adding the spike in the positivity rate was largely confined to 20 ZIP codes, where the rate went as high as 30 percent, in contrast with the rest of the state, where the rate remained around 1 percent.

The statewide positivity rate began to creep up over the weekend, when officials reported rates just slightly above 1 percent; hospitalizations have also risen over the last several days, according to state statistics. On Monday, the state reported that 543 people were hospitalized as a result of the disease, another slight increase. In recent weeks, areas in the Hudson Valley and some city neighborhoods have seen an increase in new cases and hospital admissions, according to state officials.

Mr. Cuomo stressed that “mask compliance is important,” and urged local governments to enforce mask rules and prohibitions on large gatherings, even if residents were feeling “compliance fatigue.” On Wednesday, New York City will allow indoor dining to resume at 25 percent.

In July, the state began requiring travelers from states with increasing cases to quarantine for 14 days upon their arrival in New York, though the enforcement has been loosely enforced. On Monday, Mr. Cuomo said he would sign a new executive order subjecting most travelers from other countries to the 14-day quarantine.

NYTIMES

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