The SDLP has refuted claims that plans by the Irish police to close the border to non-essential travel from 7am on Monday amounts to a 'hard border'.
Unionist politicians, however, said the Garda action undermined Irish Government claims the border could not be policed.
Northern Ireland holiday makers heading to Dublin airport could be hit with a €100 fine from Monday and the new measures will apply to anyone who is "not ordinarily resident" in the Republic.
Buses and trains will also be checked, a Garda spokesperson said, and stressed that fines will be only be enforced as a last resort.
The force explicitly warned that travel to airports to go on holiday was "non-essential".
"An Garda Síochána is also continuing to conduct checkpoints on access roads to airports and ports, as well as in departure areas, to check on whether people travelling to these locations are undertaking an essential journey.
"Travelling to an airport or port to take a holiday abroad is not an essential journey," the Garda said in a statement.
The force said if enforcement is required a fixed payment notice for €100 will be issued to each person who is in breach of the regulation.
The new rules mean the Garda can turn back day-trippers from Northern Ireland.
Under the Republic's current Covid-19 restrictions, travel is restricted to within 5km of a person's home except for essential reasons.
People travelling to an airport or port to take a holiday abroad may also be liable for a €500 fine.
Matthew O’Toole MLA, the SDLP Brexit spokesman, denied claims the move amounts to a hard border on the island of Ireland.
"Garda are enforcing rules on non-essential travel rules - as they are also doing between counties in the Republic - is clearly not a hard border.
"Constantly amping up misinformation like this helps no one," he said.
East Belfast MP Gavin Robinson, however, said: "This is a bit awkward for Simon Coveney and the 'no hard border' sledgehammer brigade.
"Seems like the RoI government is taking a decent go at hardening the existing international border between their country and Northern Ireland.
"It would seem the Republic can enforce a north-south border when it suits - which once again blows apart their arguments about the NI Protocol and it also demonstrates how hollow their antics have been for the last four years.
"The Irish position was never about the Belfast Agreement or peace. It was entirely self-serving.
"The border deniers will have been left scratching their heads on this one," the MP said.
UUP MLA Doug Beattie said the Garda move was "a game-changer".
"We have been told for four and a half years that not only can we not have a hard border, we cannot have a single camera on the border," he said.
"Within the past week we have seen that the EU is prepared to instigate a hard border and today we find the Garda are ready, willing and able to secure the border from 7am on Monday.
"This is an absolute game changer and means that the entire Brexit negotiations took place under false pretences. Given the fiasco that the Protocol has turned out to be, it is now time to reassess the situation.
"A border was put in the Irish Sea to placate those who promoted veiled threats of a potential return to violence should the hardening of the land border be considered. That has now been exposed as a sham. We must now negotiate an agreement which restores the trading links with the rest of the UK and undoes the damage done to the Belfast Agreement by the Protocol."