It has also warned that the coronavirus situation is changing rapidly - and it is not receiving information about changes in advance from the Government.
In a letter seen by The Scarborough News understood to have been sent to all of the county’s primary schools, the county council’s Corporate Director for Children and Young People's Service, Stuart Carlton, said: “As things currently stand, the local authority encourages school leaders to follow the official DfE guidance which is that primary-aged children should be returning to school this week.
“However, we are aware that some of the classroom teacher unions are advising their members of their individual right to invoke the protection of Section 44 of the Employment Relations Act.
“As such, you may find it prudent to establish which staff are available for work so that you are able to complete necessary risk assessments and make appropriate decisions as to whether you will be able to open safely.
“If, because of this, or due to coronavirus-related staff absence, you are unable to open and you decide to move to remote learning, the local authority will support that decision.
“We do ask though that you remain open to children of critical workers and vulnerable children, wherever possible.
“It feels as if we are entering a period of rapid change; local authority officers will endeavour to keep you informed as we ourselves hear of changes.
“We are not being provided with any advance notification by the Government or the DfE.”
Education staff unions are urging the Government to postpone the return of pupils to classrooms, with the NEU, which represents the majority of teachers and more than 450,000 school staff in the UK, telling its members it is not safe for them to return to school until mid-January at the earliest.
They say escalating rates combined with the new variant of the disease means opening primary schools poses an increased risk to the health of their members and contributing to the spread of the virus.
Secondary schools are staying closed this week except for vulnerable and key workers' children.
In some Tier 4 areas with very high levels of coronavirus, including across London, primary schools are also not open to most pupils.