It is not believed that the woman was contagious on her flight to New York or in the private car she took home from the airport. Still, officials said, they were trying to identify people who may have come into contact with her.

The state is instituting new testing and cleaning protocols.

In the previous month, nine people from New York City were declared free of the virus after they were tested by the Centers for Disease Control and Prevention.

Over the weekend, that testing protocol changed. Previously, the state could not test patients locally; it had to send samples to the C.D.C., in Atlanta. Now health officials in Manhattan and Albany can perform the tests, allowing for quicker results and more control over who is screened.

Mr. Cuomo said yesterday that he hoped that 1,000 samples could soon be tested per day.

He also said New York’s public health system was focused on reducing the spread of the outbreak. The state will begin new cleaning protocols in crowded public places, including schools and buses, he said.

Mr. de Blasio said the city had some 1,200 hospital beds that could be made available for coronavirus patients. He said that people who suspected they had the virus should contact 311 or go to a public health facility.

The outbreak could affect tourism.

NYC & Company, which monitors tourism in the city, has projected 285,000 fewer visitors this year from China. That would be a decline of more than 25 percent from the 1.1 million Chinese visitors last year.

China is the second-biggest source of international tourists to the city, behind Britain.

Through last weekend, restaurants, museums and Broadway shows were largely unaffected. But many stores became flooded with customers seeking supplies such as hand sanitizer, masks and antibacterial wipes. Several stores had run out of these items.