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Also, nonpublic schools and child care centers will be forced to close if they do not adhere to safety measures.

The citywide positivity rate has major implications for the public school system. Under current guidelines, classrooms will close if the test positivity rate exceeds 3 percent over a seven-day rolling average. Mr. de Blasio said on Tuesday that he would not seek to change those guidelines to target specific areas that had seen an uptick.

The mayor said that the current seven-day average was 1.38 percent, and that the city had not seen an increase in cases in schools in the nine ZIP codes in question.

If schools are forced to close, it could take weeks for them to reopen, according to the city’s health officials.

“The goal is to be under 3 percent in a way that is consistent,” Mr. de Blasio said.

But he cautioned that the city was not yet near that point.

Plans to introduce indoor dining in the city on Wednesday will not be affected, the mayor said.

Early last week, city health officials warned residents of several areas — including Gravesend, Borough Park and Midwood in Brooklyn — that strict lockdown measures would be enacted if they did not see a larger effort to follow coronavirus safety measures.

Last week, the city health department threatened to ban gatherings of more than 10 people if improvement was not seen quickly. That restriction has not been implemented so far.