Humberside Police has said it is investigating the emails which were sent in support of the vandalism of the rainbow flag in Bridlington.
The force has said it will not tolerate hate crimes after the LGBT symbol was targeted while it flew at the town's police station.
Group claims it cut down rainbow flag
A statement said: "We are investigating a number of malicious emails sent to several media outlets and local high profile public servants.
"Our investigations will also cover damage to the flag pole which carried the Pride rainbow flag on the Bridlington police station, which was raised in support of Hull Pride and damaged on Saturday. We are pleased to report that the flag has now been found.
"As all of the rainbow flags were due to be taken down from our police buildings today we have no plans to replace the one at Bridlington."
Detective Chief Inspector Matthew Peach said, "We are treating these malicious emails as a hate crime. Everyone has the right to be safe and secure and to live free from fear or harassment. Hate incidents or crimes are based on ignorance, prejudice, discrimination and hate and have no place in our society."
Police asked anyone with information that would help with their enquiries to call 101.