On Sunday, the authorities announced the first confirmed case of the new coronavirus in New York: a health care worker who had been infected in Iran, where the illness is raging, and began exhibiting symptoms after returning home. But the health care worker had kept herself largely isolated, and the authorities expressed confidence they had the situation under control.

But the case announced on Tuesday was far more worrisome.

The authorities have little inkling of how the man, a lawyer who lives in New Rochelle but works in Manhattan, had been infected. He had traveled to Miami in February and regularly visited Israel, but had not been to any areas with widespread transmission.

Public health authorities were only beginning to tally the number of people he might have exposed to the illness.

The man became ill on Feb. 22 and was admitted to a hospital in Westchester on Feb. 27., according to Dr. Demetre C. Daskalakis, the deputy commissioner for disease control at New York City’s Department of Health.

The original diagnosis was pneumonia, according to a person who knows the patient well and who spoke on the condition of anonymity. After testing negative for the flu, he was removed from isolation, the person said. Several people visited him.

But his health deteriorated, and after several days he was transferred to NewYork-Presbyterian Hospital in Manhattan. “At that point, it was a bit of a medical mystery,” the person said.