The People Before Profit Alliance has predicted that any attempt to beef up border controls in Ireland will bring large numbers of people onto the streets.
The party also suggested that any attempts to impose stricter border controls will be torn down.
West Belfast MLA Gerry Carroll issued the warning during the British Prime Minister Theresa May's whistle-stop tour of the North.
“I want to send a clear message to Theresa May and the Tories today: if you try to implement a hard border against the will of people here, we will resist you. People will take to the streets in numbers to tear down any attempt to beef up border controls," he said.
“The overwhelming majority - North and South, Leave and Remain voters - have made clear that they do not want a hard border and Theresa May must take heed."
Mr. Carroll said the Dublin government's plans to recruit up to one thousand extra customs officials to man Irish ports was playing into the Brexiteers' hands.
“We have a message, too, for Leo Varadkar who this week announced that he will seek to employ thousands to man new border checkpoints. Varadkar must use his veto to block any attempt to install a hard border, not play puppet to any Tory or EU plan to implement one."
“PBP continue to call for a vote on any final Brexit deal. Whether people here voted to leave or remain, they should have the final say on Brexit.
"We cannot rely on bureaucrats in London or the EU to represent the interests of the people in the North. We must be allowed to decide for ourselves; anything less than this is blatantly undemocratic,” he said.