Police have said tougher laws on tackling online abuse would allow them to respond 'more robustly'.
They also said they would welcome measures that would put the onus on social media providers to take action.
A survey by the Northern Ireland Local Government Association found more than three quarters of councillors here have been subjected to abuse or intimidation.
Two-thirds said that they'd been abused or intimidated on social media, and just over half said said it had happened in person. The report calls for legislation to be developed and strengthened to improve the safety of all elected representatives. Elected representatives told UTV they know of women who have been put off standing for election.
Police have said they need support in legislation, but people should continue to report threats and intimidation.
Assistant Chief Constable Bobby Singleton said: “As a police Service we take the safety of our elected representatives extremely seriously and will continue to support them by providing crime prevention and personal security advice and investigating reports made to us on an ongoing basis.
“Policing online platforms is complex and cybercrime remains one of the fastest growing crime types.
"We would welcome measures that strengthen legislation and allow us to respond even more robustly, placing some preventative and safeguarding onus on social media providers to take action.''
ACC Singleton said people should not be deterred from reporting threats to the PSNI.
“There are still a number of powers available to us now that we can use to investigate reports of online harassment and malicious communications if someone is sending a message or other matter that is grossly offensive or of an indecent, obscene or menacing nature," he added.
“We continue to encourage all our elected representatives to report any security concerns to us in order to keep themselves, their staff and members of the public attending constituency offices safe.
“We will investigate such reports and examine all evidence available to us to pursue, where appropriate, a criminal justice outcome."
If someone falls victim to a cybercrime the Police Service of Northern Ireland advises:
Do not delete any incriminating emails, texts, or messages. These are evidence. By using your ‘print screen’ button on your computer, or taking screenshots on your phone, you can create hard copies of digital evidence.
Don’t respond directly to bullies or trolls.
Talk to someone you trust, and report to the relevant social media platform.
You can also let your mobile phone provider know if the abuse is via texts or to your phone number.
For serious suspected criminality, theft, fraud, or serious emotional or physical abuse or threats, report to the police immediately.
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