East Antrim MLA Mr Dickson was speaking after the PSNI confirmed they were examining “suspected breaches of Parades Commission determinations in Coalisland” and “un-notified processions in Ardoyne and Lurgan”.
It follows masked men parading through Lurgan on Saturday and paramilitary-style uniform being worn by marchers in Coalisland.
Mr Dickson said he was pleased to see the police would be looking into the incidents.
“These were deeply disturbing incidents that anyone who supports the rule of law would find horrifying. To see people so flagrantly supporting terrorism and seeking to inspire fear in the community is simply wrong in every way.
“I am glad the police have decided to investigate and I hope they will seek to prosecute those behind such paramilitary displays. I would urge anyone with information on them to pass it to police immediately.”