The Prime Minister said primary schools in England may be ready to reopen "in stages" - but not until 1 June at the earliest.
This could begin with Reception, Year 1 and Year 6 pupils going back.
Boris Johnson also said it's the government's "ambition" to give secondary school pupils doing exams next year at least some time with their teachers before the summer holidays.
But teachers across the region have said safety must be made priority.
Headteacher at Landywood Primary School, in Great Wyrley, Andrew Clewer, said the Government briefing failed to give any "clear steps" on exactly what schools must do before they can reopen.
He said: "Sunday's briefing will have raised many questions, which we all wish were answered.
Monday's 50-page Government document contains just a few sentences which unfortunately do not give any clearer steps of what we now must do to prepare effectively for the potential June 1 phased re-opening.
"We will continue to send work every day via email to every family while we wait for clarification on exactly what schools must do to ensure everyone is safe upon our re-opening.
"We will continue to add resources to our website to help families understand the situation and signpost them to external organisations which can be of assistance.
"There still does not appear clear signposting for families to understand when they will be expected to return back to work or when their children will be returning back to school in Years 2-5, yet both of these need to work hand in hand to support families.
"To bring our community even closer together during this time, we send a weekly newsletter with updates and resources.
"We also receive photos from families each week which create our weekly videos.
"Sunday has not calmed people's concerns regarding the next steps and it appears more guidance will be shared later this week which we will capture in this week's newsletter.
"Landywood continues to support its community strongly and is oversubscribed for reception places for September.
There are places in some year groups at Landywood available once schools re-open. If you would like to enquire about one of these places, please email firstname.lastname@example.org for more information."
Executive Principal at Ormiston Forge Academy in Cradley Heath Andrew Burns said as a secondary school headteacher he "just didn't know" what was in store.
He said: "I will say this though. Students and staff safety absolutely trumps everything. We have to be prepared before we move forward."