There were at least 36 confirmed cases in the city, Mr. Cuomo said.

[Read our latest coverage of the coronavirus outbreak in the New York area.]

The state created a ‘containment area’ in New Rochelle.

New Rochelle in Westchester County is emerging as the epicenter of the state’s outbreak, and yesterday Mr. Cuomo announced a targeted strategy to help halt the spread of the virus.

The state’s plan focuses on a “containment area” in New Rochelle with a one-mile radius centered around a synagogue believed to connect many of the cases in the cluster, officials said.

The state also planned to deploy the National Guard to the containment area to clean schools and deliver food to quarantined residents, Mr. Cuomo said.

Schools and other facilities for large gatherings like community centers and houses of worship within the area will be closed for two weeks beginning tomorrow, he said. Businesses such as grocery stores and delis would remain open.