The prime minister praised the work that had been done to prepare schools for September, The Independent reported.
At the weekend he said the country had a moral duty to get children back in school.
But Anne Longfield, the children’s commissioner for England, called for more testing in schools, in contrast to ministers who say the precautions already taken are sufficient.
Asked if all teachers and older children should be tested weekly, she told Times Radio, "I wouldn't want to say weekly, but I would want to say regularly, and that may be weekly."
"There is much less concern around children who are less than secondary age... Secondary schools, where you have bigger environment and older children, it makes sense that testing and tracking should be part of that," she added.
Last week, ministers announced extra funding for school buses to help pupils return safely.