Mr. Cuomo has left most of the details about how to actually reopen safely to individual school districts, which have spent the summer creating reopening plans to be approved by the State Education Department. Districts across the state are tentatively planning to reopen late in August or early next month. New York City is scheduled to start school on Sept. 10.

The challenges facing all districts are myriad, but especially so in New York City, the nation’s largest school system, and the only major district in America currently planning to reopen even part-time.

New York City and other districts across the state are still finalizing strategies that allow for social distancing in school buildings, trying to find enough nurses to staff school buildings, and upgrading or replacing ventilation systems in classrooms. Districts are also trying to improve their remote instruction plans, since educators did not have much time to perfect online learning when schools shuttered suddenly in the spring.

Many teachers and parents across the state have expressed alarm about returning to school buildings as the virus has spiked in other states. But families across New York say they are desperate for schools and child care centers to open so that they can return to work. About 75 percent of New York City students are low-income and many of their parents are essential workers or employees who cannot work from home.

Some local officials, including Mr. de Blasio, have indicated that they may not make a final decision whether to reopen, even part-time, until late this month or even early next month.

New York City’s system, with 1.1 million children and 1,800 schools, is planning to open on hybrid model, in which children report to school one to three days a week and learn online the rest of the time.

If New York can successfully reopen its schools, it could provide a blueprint for other districts closely watching how the city fares.