Calderdale Council has advised its schools not to reopen more widely on June 1 defying the government policy.
The council said it needed to make sure that staff and children could be properly protected first.
Calderdale councillor Adam Wilkinson, said on social media "We are keen to get more pupils back to school, but safety is of paramount importance and we have been advised by public health professionals that governments key tests have not been met."
All schools are currently closed except to vulnerable children and the children of key workers.
The Government plans to begin reopening primary schools in England from next month.
Cabinet Office Minister Michael Gove said measures were being put in place to ensure the safety of children and teachers as they returned adding there was "clear scientific and clinical advice" that it was "safe" to schools to reopen with social distancing.