Britain's counter-terror police were probing the threats made to about 15 schools in the country since yesterday.
Police across the UK have been forced to close a number of primary and secondary schools while responding to the threats, which have left parents panicked and confused.
Similar threats have been reported from some states of the US as well.
"The South West Counter Terrorism Unit is pursuing a number of lines of inquiry and has spoken to law enforcement agencies in America as part of the investigation," a South West Counter Terrorism Unit spokesperson said.
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Police Scotland said "a number of schools" in the central area received a telephoned threat and that two have been closed down.
A spokesperson said: "Police Scotland would like to reassure the public that at present these do not appear to be credible threats, however they are being taken seriously.
"Staff and police are working with local authorities and are currently searching school buildings. Some schools as a precautionary measure, have been evacuated. Significant inquiries are underway."
A Police Service of Northern Ireland (PSNI) spokesperson said that the force will liaise with others in the UK to probe if the threats were linked.
Temporary Chief Superintendent Simon Walls said: "PSNI are investigating a series of malicious communications to schools across Northern Ireland today.
"At this stage there is no information to suggest the incidents are terrorist-related, however inquiries continue to establish the facts.
"We will liaise with other UK police services who have received similar calls, to investigate who is responsible and whether these incidents are linked."