New York State is a center of the outbreak in the United States, and the number of cases has been spiking in recent days, both because the virus is spreading and because more testing is being done.

Officials on Saturday reported the first two deaths in New York State linked to coronavirus.

The state had 613 confirmed coronavirus cases, up sharply from Friday, including 269 cases in New York City. Statewide, 50 of those patients were being treated in hospitals as of Friday, including 18 who were in intensive care.

Late Saturday night, officials said that two State Assembly members from Brooklyn, Helene Weinstein and Charles Barron, both Democrats, had tested positive for the virus.

The spike in cases in New York has unsettled some health care administrators and doctors, who are mindful of what has happened in northern Italy, where in less than three weeks, the virus has inundated hospitals with patients, offering a glimpse of what countries face if they cannot slow the outbreak.

Mayor Bill de Blasio has predicted that there could be 1,000 cases in the city by next week, and some doctors are expecting many more. The fundamental question for hospitals is not how many New Yorkers will get sick during the pandemic. It is how many at any given time, and whether the hospitals will have enough beds, workers and ventilators, which the most seriously ill will need to breathe.