Mayor Bill de Blasio announced on Sunday that he would reopen public elementary schools, abruptly shifting policy in the face of widespread criticism that New York City was placing more of a priority on economic activities like indoor dining than the well-being of its children.

Mr. de Blasio said that middle and high schools would remain closed, but he also signaled that he would overhaul how the city manages schools during the pandemic, which has forced millions of children in the United States out of schools and is widely perceived to have done significant damage to their education and mental health.

The mayor said the city would abandon a 3 percent test positivity threshold that it had adopted for closing the school system, the largest in the country, with 1.1 million children. And he said the system would aim to give most parents the option of sending their children to school five days a week, which would effectively end the so-called hybrid learning system.