Ofsted chief inspector Sir Michael Wilshaw has asked for additional work to be carried out by the watchdog before final reports on the schools visited over alleged Islamic takeover plots are published.
The watchdog also announced that it has inspected a further three state primary schools in the city this week, bringing the total number of schools inspected to 21.
Ofsted inspected 15 Birmingham state schools last month at Education Secretary Michael Gove's request, plus inspections of the three schools belonging to the Park View Educational Trust.
It is expected that all 21 inspection reports will be published at the beginning of June.
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The foreign secretary has criticised internet and social media giants for failing to detect and remove extremist material posted online.