There was “no proof that closures will help stop the spread,” Dr. Katz wrote in an email to the mayor’s closest aides. He believed that banning large events would hurt the economy and sow fear. “If it is not safe to go to a conference, why is it safe to go to the hospital or ride in the subway?” he wrote. And, he said, many New Yorkers were going to get infected anyway.

“We have to accept that unless a vaccine is rapidly developed, large numbers of people will get infected,” he wrote. “The good thing is greater than 99 percent will recover without harm. Once people recover they will have immunity. The immunity will protect the herd.”

For Mr. de Blasio, the arguments in Dr. Katz’s March 10 email, obtained by The New York Times, appeared to hold sway over the calls for greater restrictions on daily life from top Health Department officials, who were alarmed by public health surveillance data pointing toward a looming outbreak.