Secondary schools must be allowed to teach pupils using a rota system to slow the rise in coronavirus cases, Preston City Council's leader has said.
Matthew Brown said the education system had become "a super spreader" and students should now spend two weeks in school followed by two remote learning.
A teaching union said schools could be "plunged into disarray" without rotas.
The Department for Education said "all possible measures" would be considered before restricting attendance".
The Preston council area, along with the rest of Lancashire, moved into the highest level of England's coronavirus restrictions on 17 October and the latest government figures showed the infection rate in the city stood at 463.9 cases per 100,000 people on 27 October, up from 450.6 cases seven days earlier.
Mr Brown said the council was "very concerned" by the rise and while schools had "done their best... having so many people together has made the education system a super spreader".
The National Education Union said if a rota system for tier two and tier three areas was not in place soon, schools would be "plunged into disarray".
A spokesman for the neighbouring Lancashire County Council said it was not currently proposing the use of a rota system, but as with all aspects of its response to the pandemic, that was "being regularly reviewed".
Government guidance issued to schools in August which stated that a four-week rota system was an "absolute last resort" as a contingency for a "worst-case scenario".
A spokeswoman for the Department for Education said it was working with a very small number of schools operating on a rota basis and "all possible measures would be explored before considering restricting attendance in education".