The PSNI is treating comments made by a protester during the Belfast Pride parade at the weekend as a hate crime.
Comments made by a man using a public address system at Royal Avenue were later reported to police.
Belfast Alliance councillor Micky Murray was present when the comments, which he said were "deeply offensive" were made.
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"Members of the public were visibly and audibly outraged by it."
The councillor intends to raise the matter with Assistant Chief Constable Bobby Singleton this week.
Superintendent Christian Bradley said: "Officers were present at the scene and gathered evidence on body worn video.
"This footage is being reviewed by investigators.
"The incident is being treated as a hate crime."