At least 98 percent of principals and 93 percent of teachers as well as 90 percent of non-education staff members had been vaccinated by Friday, city officials said. The figures are likely to change by Monday, the deadline for meeting the requirement, because more employees are very likely get shots or provide proof of vaccination over the weekend.

The Department of Education reported that more than 18,000 shots had been given to staff members since Sept. 24.

“Mandates work, they make us safer,” Mr. de Blasio said in a television interview on Friday. “I would urge every mayor in America: Do it now, get those vaccine mandates in place ahead of the cold weather, when things are going to get tougher. Do it now, or you will regret it later.”

The union that represents city teachers, which has been tracking vaccinations among its members separately, said that about 95 percent of its members had gotten at least one vaccine dose.