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

Mr. de Blasio said middle and high schools would remain closed, but also signaled that he would overhaul how the city manages the system during the pandemic, which has forced millions of children in the United States out of schools and is 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 many parents the option of sending their children to school five days a week, which would effectively end the so-called hybrid learning system for some city schools.

Students can return only if they have already signed up for in-person learning, meaning just about 190,000 children in the grades and schools the city is reopening next week would be eligible. About 335,000 students in total have chosen in-person classes.