Authorities in Scotland, Northern Ireland and the Republic of Ireland said a threatening email which was sent to a large number of schools on Wednesday was a hoax originating from outside the United Kingdom.
The emails were reported after the evacuation of at least 300 schools in Italy.
Irish police said they were aware of a "generic communication" sent to a number of schools and they had assessed that the threat was not credible and that there should be no evacuation.
Over 300 schools in Northern Ireland were also sent a threatening email which was being treated as a hoax, police in the British province said, adding that the email originated from outside the UK.
"We take incidents of this nature very seriously and we understand the concern in the community, school communities and for students and parents," Assistant Chief Constable Anthony McNally said.
Irish police noted that there had recently been "increased activity in hoax and non-credible bomb threats", and advised the public to contact officers if they receive one.
Police in Scotland said the messages were immediately assessed and treated as hoaxes.
"Our enquiries have established that there is nothing to suggest that they represent a credible threat or that there is any wider threat to the public," their statement said.

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