Dozens of schools in Hull have seen classes closed due to Covid as the city's infection rate remains the highest in England.
Director of public health Julia Weldon said 57 of the city's 97 schools have had to send some pupils home.
The city's infection rate of 776.4 per 100,000 people is more than treble the national average of 221.
Hull City Council said it wanted government permission to deliver home teaching online if necessary.
Ms Weldon said the 57 schools have seen closures in some year groups but only one primary school had been completely closed to all children "for a very short period of time".
The council said 27% of students were absent from school on Monday, double the rate of 13.5% for the rest of England.
Labour leader Stephen Brady wrote to the prime minister on Monday asking for help and claimed the city had been "forgotten" by government.
On Tuesday the authority said it had not yet received a response.
The council said it wanted to be able to close classes and deliver home teaching online, if needed, as the situation develops.
Michael Whale, from the Hull branch of the National Education Union, called for schools to close to help the city deal with the pandemic.
"A circuit breaker and a closure of schools would allow management time to reset and maybe look at running schools in a slightly different way," he said.
'Significant expansion of testing'
Ms Weldon said: "What we want is the ability, perhaps in the next phase of this pandemic response, for local schools who know their children and know their families to make those local decisions so they can maintain the best offer they possibly can."
The council said it wanted to "prioritise attendance in schools for vulnerable children and children of key workers, whilst continuing to provide education for all children through a blend of learning in school and through home and on-line learning."
The BBC contacted the prime minister's office about Mr Brady's letter and received a response from the Department of Health and Social Care.
A spokesperson said: "We are providing 600,000 lateral flow tests to areas around the country - including Hull - as part of our significant expansion of testing.
"This is on top of three extra mobile testing units that are up and running in Hull today, alongside existing walk-through and regional testing sites.
"We have also provided £2m to Hull City Council to support the current national restrictions."
They added: "Future decisions will be made on a local and regional basis according to the latest data and trends, and we will continue to work closely with local leaders."