The police commissioner, Dermot F. Shea, said 98 people in the New York Police Department, including 70 uniformed officers, had tested positive for the coronavirus. Three people have been hospitalized, and one was discharged on Sunday, he said at a news conference on Sunday.

Police officials do not believe the members of the department are contracting the virus through police work, but that officers and civilian workers are contracting it from sick family members, he said. More officers were also getting tested, he added.

“As society contracts this disease, so do we,” he said.

But two police officials said that the confirmed cases were just a fraction of the overall problem. Overall, more than 2,000 police officers and civilian aides have called out sick with flulike symptoms, according to the officials, who requested anonymity to discuss confidential police medical records.

Commissioner Shea would not give specific numbers but said the rate at which officers were calling out sick since Tuesday is approaching double the normal rate. But he said the department had not been hindered in carrying out its duties, including its new role enforcing social distancing at grocery stores, parks and other public places.

“We are not at the point where we’re close to going to 12-hour tours,” he said. “But what we are doing is planning for all eventualities and moving people from units that are less-important right now to be ready for any and all eventualities. So I think we are in a good place still and the planning is literally ongoing hour by hour.”

New Jersey has nearly 2,000 confirmed cases.