It follows Education Secretary Gavin Williamson's comments that a return to school in September would be "compulsory" and families may face financial penalties if they keep their children at home.
Speaking on Monday, June 30, Mr Williamson said: "It is going to be compulsory for children to return back to school unless there's a very good reason, or a local spike where there have had to be local lockdowns.
"We do have to get back into compulsory education as part of that, obviously fines sit alongside that.
"Unless there is a good reason for the absence then we will be looking at the fact that we would be imposing fines on families if they are not sending their children back."
However, Councillor Jonathan Pryor, Executive Member for Learning, Skills and Employment at Leeds City Council said that the government should publish its plan before "threatening families".
Coun Pryor said: "We have been working hard alongside all schools in Leeds to enable them to welcome back more pupils and to build confidence in children returning safely to school.
"While the Government have said that it will be compulsory for all pupils to be back at school from September they are yet to publish their plan as to how this will actually work.
"Schools, pupils and parents will understandably have questions around social distancing, space within school and even things as basic as how pupils will physically get to and from school safely.
"I think the Government need to get the basics in place and rebuild confidence before they start threatening families with fines."
Geoff Barton, general secretary of the Association of School and College Leaders (ASCL), has called for a "period of grace" before fining parents if they refuse to send their children back to school when they fully reopen.
He said: "We don't think that it is the right approach to fine parents for the non-attendance of children as soon as schools fully reopen in September, and the government should not expect schools to take this action.
"There will be many frightened and anxious parents out there, and this is very much a case of building confidence that it is safe to return, rather than forcing the issue through the use of fines.
"The Government must show a greater understanding of the realities of the situation, and we would recommend that there is a period of grace while normal patterns resume."
Some children began returning to school at the beginning of this month - but the government said that parents who did not feel safe sending their children back to school would not face fines.
Attendance was around a quarter (26%) in Year 1, up from a fifth the previous week, and 29% in Reception, up from 22% on June 11, the figures show.
The government's plan for the autumn return to school will be published at the end of week, the Education Minister said.
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