Humberside Police said the threats were hoaxes that have been issued across the country.
It comes as the NCA confirmed it was investigating "potential similarities" to emails sent to hundreds of schools last month.
Humberside Police said community officers were sent to schools today "to provide reassurance".
The latest threats come after more than 400 schools and colleges across the country were reported to have received similar emails last month.
Last month two teenagers, from Abbots Langley in Herefordshire and Watford, were arrested as part of an ongoing NCA investigation.
In a statement this evening the NCA said: “A number of schools and colleges have received threatening emails today.
“We understand these threats have caused considerable concern and are taking the incident extremely seriously, but we would stress we do not assess there to be an increased risk to the public.
“Given that for many schools and colleges it is the last day of the Easter break, some schools may not yet be aware of the email.
“Potential similarities to malicious emails sent to schools since the beginning of March are being considered by an ongoing NCA investigation.
“An 18-year-old men from the Abbots Langley area and a 19-year-old man from Watford have been arrested in that investigation, both on suspicion of offences relating to malicious communications.
"They were later released under investigation.”
Around 20 schools, including Bay Primary in Bridlington, closed after receiving the emails.
Detective Chief Inspector Stewart Miller, of Humberside Police, said earlier today: "We’ve been made aware of a hoax email sent to schools in the force area this morning 13 April 2018.
"We want to categorically reassure parents and children, staff and the wider public that this a non-credible threat that has been sent nationwide.
"Our primary concern is to ensure that schools are given guidance, up-to-date information and reassurance and above all that everyone is safe.
"Community officers have already been sent to schools to provide that reassurance."