About 6,300 schools had received bomb warnings on Wednesday, when the alarm was more widespread and panic spread among parents, Reuters reported.
Schools across Italy received bomb threats for a second straight day on Thursday, forcing fresh evacuations even as officials said the response was far more limited than a day earlier.
The prime minister's office said 3,778 schools received hoax bomb warnings on Thursday, but only 77 were evacuated, some of them only briefly, Reuters reported.
The back-to-back alerts left parents and school staff facing a second day of disruption over warnings that authorities have treated as hoaxes.
The government told schools that buildings should not be evacuated solely because of a mass email warning of danger, in the absence of concrete evidence beyond that message.
Authorities said that guidance marked a change from the previous day, when evacuations were far more common.
A government minister said the hoax threats against schools posed no risk to the public.
The BBC reported that searches had found no devices.
The school warnings followed a series of bomb hoaxes last week against airports and airlines in several European countries, the BBC reported.
A number of those threats were claimed by an extremist misogynistic group, which later denied any link to the false warnings.
Separately, a Russian extremist group denied sending the hoax bomb threats.