Police are understood to be probing an alleged threat against DUP leader Arlene Foster.
The comment is reported to have been posted under an article about a murder on social media, with the man adding "to see if I’d get away with it".
Democratic Unionist Councillor Keith Elliott said in a statement to the Impartial Reporter: "Arlene Foster has been the subject of online attack and harassment throughout her political career.
"These particular comments have been reported to the PSNI, and despite their vicious nature, we will not comment further until the PSNI has carried out their investigation."
A PSNI spokesperson said: "We do not discuss the security of individuals and no inference should be drawn from this.
"However, if we receive information that a person's life may be at risk we will inform them accordingly. We never ignore anything which may put an individual at risk."
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