At an elementary school in Mito, Ibaraki Prefecture, some 230 students took part in a ceremony marking the start of the new academic year.
Schools in Tokyo and other areas where infection counts are growing remained closed and were expected to stay that way for at least another month.
In Kyoto, where elementary schools are scheduled to resume on Wednesday, Megumi Aoyama, 34, welcomed the move, saying she was worried that the further prolonging of school closures would affect her daughter who enters elementary school this year.
Ryoko Nishioka, 42, who has three children attending an elementary school in the city of Kochi said she does not feel the school is safe during the virus crisis.
I am afraid of the coronavirus, but we are reaching our limit living like this," she said.